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Finding Factors of Numbers Interactive Question Generator

What is a factor of a number

Factors are numbers that divide exactly into another number, which is called the multiple.

Factors can be multiplied to make the multiple.

4 × 2 = 8 and so, both 4 and 2 are factors of 8.

Factors often come in factor pairs which are the two numbers that multiply together to make the multiple.

4 and 2 are factor pairs for 8 because they multiply to make 8.

1 × 8 = 8 and so, 1 and 8 are both factor pairs of 8.

The factors of 8 are: 1, 2, 4 and 8.

A factor is a number which divides exactly into the number that it is a factor of.

Finding factors of a number example of finding factors of 16

If a number is a factor of another number, it will divide into the other number exactly without remainder.

We will find the factors of 16.

We start with 1 because 1 is a factor of every number.

1 × 16 = 16 and so, 1 and 16 are factor pairs of 16.

We now try the next number: 2.

2 × 8 = 16 and so, both 2 and 8 are factor pairs of 16.

3 does not divide exactly into 16 and so, it is not a factor.

4 × 4 = 16 and so 4 is a factor of 16.

4 pairs with itself so it does not have another number as its factor pair.

We have arranged the numbers from smallest to largest around the sides of 16, writing each factor pair at a time.

When the numbers in this circle meet in the middle we have found all of our factors.

The factors of 16 are 1, 2, 4, 8 and 16

Supporting Lessons

Finding Factors Calculator

Enter the number below to find all of its factors:

Finding Factors of Numbers Interactive Questions

Finding Factors of Numbers Worksheets and Answers

How to Find Factors of a Number

What is a Factor of a Number

A factor is a number that divides exactly into another number.

what is a factor 4 x 2 = 8

The larger number that factors divide into exactly is called the multiple. Factors can be multiplied by a whole number to make this multiple.

In the example above, both 2 and 4 are factors of 8 because they can be multiplied to make 8. 8 is therefore both a multiple of 2 and a multiple of 4.

What are Factor Pairs?

Factor pairs are two whole numbers which multiply together to make another whole number. Both numbers are factors of the number that they multiply to make. This means that they divide exactly into this number without a remainder.

Factor pairs and multiples of 8

In the example above, both 2 and 4 are factor pairs which multiply to make 8.

All factors come in pairs except for the square root factor of square numbers.

For example, we will look at the list of all factors of 16 below.

list of all Factor pairs of 16

1 is a factor of every number because it divides exactly into every number. 1 is a factor pair with the number itself.

1 × 16 = 16 and so, the first factor pair of 16 is 1 and 16.

2 × 8 = 16 and so both 2 and 8 form a factor pair of 16.

4 × 4 = 16 and so 4 does not form a factor pair because it does not multiply by a different number to make 16.

All factors come in pairs except for square roots of the number itself. A square root is the number that is multiplied by itself to make the given number.

4 is the square root of 16, which means that 4 multiplied by itself makes 16. And because 4 is the square root of 16, it does not form a factor pair with another number.

Here are the factor pairs of 12.

Factor pairs of 12

6 × 2 = 12

3 × 4 = 12

1 × 12 = 12

Each of the factors of 12 come in pairs.

How to Find Factors of a Number

To find factors of a number, use the following steps.

Write down the number 1 and the given number at each end of a list.
Try dividing all of the numbers that come after 1 into the larger number.
If these numbers divide exactly into the given number with no remainder, then they are factors.
Write down each number that divides exactly along with the answer to the division.
Write these numbers in ascending order in the list.
Stop when you reach the square root of the number itself or another number on the list.

When teaching finding factors of numbers, it can be useful to write the given number itself in the centre and write the factors around the outside.

In this example we will find a list of all factors of 18.

We first write down the number 1 and the given number, 18. We write 1 at one end and 18 at the other end. We will put any other factors in between.

1 and 18 are factor pairs of 18

This is because 1 × 18 = 18. 1 is always a factor of every number and so is the number itself.

We will now try the numbers that come after 1, such as 2, 3, 4, 5 and so on.

2 × 9 = 18 and so, both 2 and 9 are factors of 18. We write down the 2 after the 1 in our list and we write the 9 before the 18 on our list.

1, 2, 9 and 18 are factors of 18

9 will be the second biggest factor in our answer list after 18. We now know that no numbers between 9 and 18 will be on this list of factors.

We now try 3.

3 × 6 = 18 and so, we write down both 3 and 6 on our list of factors.

1, 2, 3 ,6, 9 and 18 are all of the factors of 18

We write 3 after the 2 and we write the 6 before the 9.

We now try 4.

4 does not divide exactly into 18 and so it is not a factor of 18. We do not write it down.

5 does not divide exactly into 18 either.

The next number after 5 is 6, but 6 is already on our list of factors because it paired with 3.

a list of all factors of 18

Since we have now reached numbers that are already on our list we can stop as we know that we have found every factor of 18.

The factors of 18 are: 1, 2, 3, 6, 9 and 18.

Now try our lesson on Multiples of Numbers where we learn how to find multiples of a number.

Multiples of Numbers

How to Find Multiples

the first 5 multiples of 5

The multiples of a given number are the numbers that are in the times tables of that number.

1 × 5 = 5 and so, the first multiple of 5 is 5.

2 × 5 = 10 and so, the second multiple of 5 is 10.

3 × 5 = 15 and so, the third multiple of 5 is 15.

4 × 5 = 20 and so, the fourth multiple of 5 is 20.

5 × 5 = 25 and so, the fifth multiple of 5 is 25.

There are an infinite number of multiples.

For example the hundredth multiple of 5 is 500.

The multiples of a number can be found by repeatedly adding that number.

For example, 5, 10, 15, 20 and 25 are found by starting at 0 and adding 5.

To find a multiple of a number, multiply the number by any whole number.

listing the multiples of 6

The first few multiples of 6 are the numbers in the 6 times table.

The multiples of 6 can be found by counting up in sixes starting from 0.

1 × 6 = 6 and so, the first multiple of 6 is 6.

2 × 6 = 12 and so, the second multiple of 6 is 12.

3 × 6 = 18 and so, the third multiple of 6 is 18.

4 × 6 = 24 and so, the fourth multiple of 6 is 24.

5 × 6 = 30 and so, the fifth multiple of 6 is 30.

Supporting Lessons

Listing Multiples: Interactive Questions

Listing Multiples Worksheets and Answers

Multiplying by Multiples of 10 and 100

Finding Multiples of Numbers

What are Multiples?

Multiples are the numbers formed by multiplying a number by any other number. In simple terms, multiples of a given number are any numbers that are in the times tables of this number. For example, the multiples of 2 are 2, 4, 6, 8, 10, 12 and so on.

Many multiples are multiples of more than one number.

Here we can see that 6 is both a multiple of 2 and a multiple of 3.

This is because 2 × 3 = 6 and 3 × 2 = 6.

6 is a multiple of 2 and 3

6 is the third multiple of 2 and 6 is the second multiple of 3.

In any multiplication sentence, the numbers being multiplied together are the factors of the answer. This means that they divide exactly into the answer.

what are factors and multiples

In any multiplication sentence, the answer is a multiple of the numbers being multiplied together.

3 x 2 = 6 showing factors and multiples

How to Find Multiples of Numbers

To find multiples of a number, multiply the number by any whole number. For example, 5 × 3 = 15 and so, 15 is the third multiple of 5.

For example, the first 5 multiples of 4 are 4, 8, 12, 16 and 20.

listing multiples of 4

1 × 4 = 4, therefore the 1st multiple of 4 is 4.

2 × 4 = 8, therefore the 2nd multiple of 4 is 8.

3 × 4 = 12, therefore the 3rd multiple of 4 is 12.

4 × 4 = 16, therefore the 4th multiple of 4 is 16.

5 × 4 = 20, therefore the 5th multiple of 4 is 20.

The first 5 multiples of 4

We can see that the multiples of 4 increase by 4 each time.

To list multiples of a number, start at zero and keep adding this number. The multiples of any given number always have a difference between them that is equal to the given number. If you know a multiple of a number, you can find the next multiple by adding the number to it.

Here we will list the first five multiples of 6.

We can start from 0 and count up in sixes.

The first five multiples of 6 are 6, 12, 18, 24 and 30.

listing the multiples of 6

We can see that 6 + 6 = 12, 12 + 6 = 18, 18 + 6 = 24 and 24 + 6 = 30.

We can also find the multiples of 6 by multiplying 6 by any number.

1 × 6 = 6, therefore the 1st multiple of 6 is 6.

2 × 6 = 12, therefore the 2nd multiple of 6 is 12.

3 × 6 = 18, therefore the 3rd multiple of 6 is 18.

4 × 6 = 24, therefore the 4th multiple of 6 is 24.

5 × 6 = 30, therefore the 5th multiple of 6 is 30.

In this next example, we will list the first five multiples of 8.

We can start at zero and count up in eights.

The first five multiples of 8 are 8, 16, 24, 32 and 40.

8 + 8 = 16, 16 + 8 = 24, 24 + 8 = 32 and 32 + 8 = 40.

listing the first 5 multiples of 8

We can also find the multiples of 8 by multiplying 8 by any number.

1 × 8 = 8, therefore the 1st multiple of 8 is 8.

2 × 8 = 16, therefore the 2nd multiple of 8 is 16.

3 × 8 = 24, therefore the 3rd multiple of 8 is 24.

4 × 8 = 32, therefore the 4th multiple of 8 is 32.

5 × 8 = 40, therefore the 5th multiple of 8 is 40.

Lists of Multiples

Here is a list of the first 12 multiples of the first 12 numbers:

The multiples of 1 are 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11 and 12.

The multiples of 2 are 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22 and 24.

The multiples of 3 are 3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33 and 36.

The multiples of 4 are 4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44 and 48.

The multiples of 5 are 5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55 and 60.

The multiples of 6 are 6, 12, 18, 24, 30, 36, 42, 48, 54, 60, 66 and 72.

The multiples of 7 are 7, 14, 21, 28, 35, 42, 49, 56, 63, 70, 77 and 84.

The multiples of 8 are 8, 16, 24, 32, 40, 48, 56, 64, 72, 80, 88 and 96.

The multiples of 9 are 9, 18, 27, 36, 45, 54, 63, 72, 81, 90, 99 and 108.

The multiples of 10 are 10, 20, 30, 40, 50, 60, 70, 80, 90, 100, 110 and 120.

The multiples of 11 are 11, 22, 33, 44, 55, 66, 77, 88, 99, 110, 121 and 132.

The multiples of 12 are 12, 24, 36, 48, 60, 72, 84, 96, 108, 120, 132 and 144.

Now try our lesson on Multiplying by Multiples of 10 and 100 where we learn how to multiply by numbers in the 10 and 100 times table.

How to Subtract Positives from Negatives Using a Number Line

Supporting Lessons

Subtracting from Negative Numbers: Worksheets and Answers

How to Subtract a Positive from a Negative Number using a Number Line

Below we have the calculation ‘3 + 4’.

Both 3 and 4 are positive numbers. We can show that they are both positive by writing a plus sign in front of each number.

However, plus signs are not necessary to show that a number is positive.

It is assumed that a number is positive unless a minus sign is written in front of it.

3+4=7 shown on a number line

The plus sign means that we move in the positive direction, which is to the right on the number line.

The ‘+3’ means that we start at 0 and move three places to the right.

3+4=7 shown on a number line

The ‘+4’ means that we move another four places to the right.

We have moved a total of seven places to the right on our number line.

So,

3 + 4 = 7

In the calculation below, we have ‘- 3 – 4’.

-3 - 4 = -7 shown on a number line

The minus sign means that we move in the negative direction, which is to the left on the number line.

The ‘-3’ means that we start at 0 and move three places to the left.

-3 - 4 = -7 shown on a number line

The ‘-4’ means that we move another four places to the left.

We have moved a total of seven places to the left.

So,

– 3 – 4 = – 7

-3 - 4 = -7 shown on a number line

In both calculations, we moved a total of seven places.

The positive signs meant that we moved a total of seven places to the right.

The negative sign meant that we moved a total of seven places to the left.

We moved 3 left and 4 left to move 7 places left on our number line.

Lesson: Finding the Mean

The Counting On Strategy for Addition

Addition using the Compensation Strategy

Counting on strategy for addition on a number line summary of counting on from the largest number

Here we are asked to add 4 and 12 using a number line.

This means that we start at 4 and move 12 places to the right – we count on 12 more.

It is important to make sure that we count the number of jumps until we get to 12.

4 + 12 = 16, however it is possible that we may make a mistake in counting 12 jumps.

In the counting on strategy it is best to start with the largest number, which is 12.

Instead of 4 + 12, we can look at 12 + 4, which only involves 4 jumps.

Starting at 12 and counting on 4 jumps, we still arrive at 16.

The order of the addition does not matter and so it is easiest to start with the largest number when using this addition strategy.

Start at the largest number in the addition on the number line.

Move right along the number line by the smallest number in the sum.

Adding on from Largest Number example of using the counting on strategy for addition

We have the sum of 3 + 15.

In the counting on strategy we start with the largest number, so we rearrange this addition to be 15 + 3.

We start at the largest number, which is 15 and we mark this on our number line.

The smallest number in the addition sum is 3 and so we will make 3 jumps along the number line to the right.

We count on 3 jumps from 15, making sure that it is the number of jumps that we count.

We arrive at 18.

3 + 15 = 18.

Supporting Lessons

Counting On Addition Strategy Worksheets and Answers

counting on strategy for addition worksheet pdf

The Counting On Strategy for Addition

What is the Counting On Strategy?

The counting on strategy means to start with the biggest number in an addition and count on from there. For example, with 3 + 4 we start with 4 and then count on 3 more. Counting 5, 6, 7 is quicker and easier than starting at zero and counting 1, 2, 3, 4, 5, 6, 7.

The counting on strategy is a method used for improving the speed and accuracy of basic addition. It is introduced to children once they have understood the concept of numbers and their order on a number line.

The counting on strategy may appear obvious but it is not intuitive for a small child who first starts counting objects.

Here is an example of using counting on to add 4 + 3.

counting on strategy example of 4 add 3

We start at the largest number of 4. We then simply add 3 more from here. The next 3 numbers are 5, 6 and 7.

Therefore 4 + 3 = 7.

We will now compare this to what a child might do without learning the counting on strategy for addition.

If a child does not know how to count on, they will simply start at 0 and count the first number and then count the second number on top of this.

For example, the child would not start at 4 but instead count up from 0 to 4.

counting up to 4 counters

Provided that we know which number comes after 4 and the sequence of numbers leading on from four, we can count on from this point.

We arrive at 7.

It is quicker to start at the larger number and count on three more.

Rather than simply counting all the way up to seven, we can start at four and count on three more.

Counting On using a Number Line

We can use a number line to help us with the counting on addition strategy for larger numbers.

Our first example on the number line below is 4 + 12.

Addition of 4 + 12 = 16 shown by counting on a number line

To work this addition out, we could start with 4 and add on 12. However, this involves a lot of jumps on our number line and is not very efficient.

We can see that we start at 4 and make 12 jumps to arrive at 16.

We can already see that counting up to 4 and then 12 more is quite a long procedure and it is possible that we will make a mistake in our counting. It can be common for children to miscount when they are adding on larger numbers.

When using the counting on strategy, it is easier to start with the largest number and add on the smaller number.

The addition 12+4=16 shown on a number line

We start with the largest number of 12 and add on the smaller number of 4.

We can circle or underline the starting number to help us. In our example, we have coloured it in red.

When teaching the counting on addition method, it is important to emphasise that we are counting the number of jumps we have made to the right along the number line. We count the number of jumps after we have completed each jump and arrive at the next number.

We count 4 jumps.

This takes us to 16.

12 + 4 = 16

And so,

4 + 12 = 16

Children may commonly make mistakes with the counting procedure, particularly if they count the numbers on the line, rather than the jumps. A common misconception is that they may include the starting number as one of the 4 numbers that they have added.

It is best to reinforce that it is the number of jumps that we are counting and when teaching this, you could move your finger or a toy along the number line as you say each number, only saying each number as you arrive at it.

Here is another example of using the counting on addition strategy.

We have 4 + 14.

Remember that we do not want to be using the counting on strategy to count on with a large number. It will be more difficult to do this without making a mistake in the counting.

counting on strategy of addition example of 4 + 14

We will instead count on from the largest number in the addition sentence.

The largest number is 14 and so we will start here.

Instead of 4 + 14, we will calculate 14 + 4.

counting on addition strategy example of starting with the largest number and counting on

Remember that we can circle, underline or highlight the starting number of 14. If working with a number line in front of you, you can put your finger or a toy at 14.

We will count on 4 more to add 4. This is counting 4 jumps to the right.

counting on strategy 3.png

We arrive at 18.

Therefore, 14 + 4 = 18

And so, 4 + 14 = 18

Now try our lesson on Addition using the Compensation Strategy where we learn another addition strategy, the compensation strategy.

addition compensation strategy

Addition using the Compensation Strategy

Compensation Addition Strategy: Interactive Questions

addition strategy compensation method using number bonds to add two numbers

We want to add 7 + 8.

Instead of 7 + 8, we will work out 7 + 10.

7 + 10 = 17.

From our
number bonds to 10Pairs of numbers that add to make 10.
, 8 is two less than 10.

Since 8 is two less than 10, we need to subtract 2 from 17.

7 + 8 = 15.

Adding ten and then subtracting two is easier than trying to add 8.

This is addition by compensation.

compensation strategy of addition example

We want to find 15 + 18.

It is easier to add 20 to 15 than it is to add 18.

15 + 20 = 35.

20 is two more than 18 so we have added 2 more than we needed to.

We subtract two to compensate. So 35 – 2 = 33.

15 + 18 = 33.

Supporting Lessons

Compensation Addition Strategy Interactive Questions

Compensation Addition Strategy Worksheets and Answers

Mental Addition of 2-Digit Numbers

What is the Addition Strategy for Compensation in Maths?

The compensation method is an addition strategy in which we add a larger number than we are required to add and then we subtract the extra amount afterwards.

We will look at addition examples in which we add numbers in the ten times table first. We will start by using our

to help us.

Number Bonds to 10

In our first addition example below, we are asked to add 6 + 7:

We can instead work out 6 + 10, which equals 16.

This was an easier addition since the units remain as six, we just add an extra ten in front.

Looking at our number bonds to ten, we can see that 10 is three larger than 7.

We have added three too many.

We will subtract 3 from 16 to get our final answer.

16 – 3 = 13

Therefore 6 + 7 = 13.

This method of adding more than we need and then subtracting the difference at the end is known as the addition compensation strategy.

Now that we have understood how to use the compensation method with our number bonds to ten, we will extend the strategy to look at adding larger numbers.

For example, in the addition example below, we have 15 + 18.

15 + 18 using the compensation strategy for addition

To make this addition calculation easier we can add 2 to 18 to make our next multiple of ten, which is 20.

addition by compensation 15+18 by adding 20 and subtracting 2

15 + 20 = 35

Because we added 2 at the beginning, we now need to subtract 2 from our answer to compensate.

15+18 by adding 20 and subtracting 2 with compensation

35 – 2 = 33

Therefore,

15 + 18 = 33

With practice, the compensation method can be used as a mental addition strategy to quickly add 2-digit numbers.

Now try our lesson on Mental Addition of 2-Digit Numbers where we learn how to quickly add 2-digit numbers in our head.

Area of Compound Shapes with Rectangles

finding the area of a composite rectangle

A compound shape is a more complicated shape made up of several simpler shapes.

This shape is made up of two rectangles.

To find the area of a compound shape, find the areas of the simpler shapes and add them together.

We first split this shape into 2 rectangles.

The area of a rectangle is base × height.

The leftmost rectangle area is 5 × 3 = 15 cm².

The rightmost rectangle area is 2 × 6 = 12 cm².

We add the two rectangle areas to find the total area.

15 cm² + 12 cm² = 27 cm².

Find the area of each rectangle by multiplying its base by its height.

Add the areas of the rectangles together to get the total area.

Area of compound shapes example with rectangles

We split this composite shape into 2 rectangles.

The area of each rectangle is base × height.

The area of the left rectangle is 6 × 12 = 72 cm².

We need to find the base of the rectangle on the right.

We can see that the horizontal distance of 6 plus the missing side must equal 14 cm.

14 – 6 = 8 cm and so the base of the right rectangle is 8 cm.

The area of the rightmost rectangle is 8 × 8 = 64 cm².

We add the areas of the two rectangles to find the total area.

72 + 64 = 136 cm².

Supporting Lessons

Area of a Rectangle

Area of Compound Shapes Worksheets and Answers

area of compound shapes worksheet answers pdf