Integers, Factors, Multiples, Rational Numbers

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MULTIPLES

If a number is a multiple of another number, it means that it can be made out of adding groups of the other number together.

Examples

12 is a multiple of 4 because 4 + 4 + 4 = 12 (or 4 x 3 = 12)

27 is a multiple of 9 because 9 + 9 + 9 = 27 (or 9 x 3 = 27)

17 is not a multiple of 4 because it cannot be made by adding groups of 4 together.

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FACTORS

A factor is a number that divides into another number with no remainder.

In other words every number is divisible by each of its factors.

1 is a factor of every whole number, because every integer is divisible by one.

Examples

3 and 7 are both factors of 21 because 3 x 7 = 21

10 and 6 are both factors of 60 because 10 x 6 = 60

7 is not a factor of 24 because 24 is not divisible by 7 (24 ÷ 7 = 3 remainder 3).

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Multiples and Factors are connected with each other:

• if we know that 3 is a factor of 12, then 12 is a multiple of 3

• if we know that 33 is a multiple of 11, then 11 is a factor of 33.

• also, if we know that 24 is not a multiple of 7, then 7 is not factor of 24.

The example below shows the relationship visually.

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Read three times:

If we know that 3 is a factor of 24, then 24 must be a multiple of 3.

If we know that 24 is a multiple of 3, then 3 must be a factor of 24.

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Which is a factor of 12?

• 5, 7, 8, 9, 10, 11

• 2, 4, 8, 10, 16, 20

• 1, 3, 5, 7, 9, 11

• 1, 2, 3, 4, 6, 12

What is a multiple of 5?

• 2, 4, 6, 8, ...

• 3, 6, 9, 12, ...

• 7, 14, 21, 28, ...

• 5, 10, 15, 20, ...

Find the factors of 24.

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Find the multiples of 8.

• 8, 16, 24, 32, 40, 48, 56, 64, 72, 80, ...

• 6, 14, 22, 30, 38, 46, 54, 62, 70, 78, ...

• 4, 12, 20, 28, 36, 44, 52, 60, 68, 76, ...

• 10, 20, 30, 40, 50, 60, 70, 80, 90, 100, ...

Is 15 a factor of 45? (Yes/No)

• Maybe

• No

• Yes

• Sometimes

Is 10 a multiple of 3? (Yes/No)

• No

• Maybe

• Yes

• Sometimes