What are Multiples?

Multiples of any number are formed by multiplying that number by an integer. For example, you want to find the multiples of 6. You can do that by multiplying 6…

Multiples of any number are formed by multiplying that number by an integer.

For example, you want to find the multiples of 6.

You can do that by multiplying 6 by other integers.

6 × 1 = 6; 6 × 2 = 12; 6 × 3 = 18; 6 × 4 = 24; 6 × 0 = 0; 6 × -2 = -12….

So the multiples of 6 are 0, ±6, ±12, ±18, ±24….etc.

Similarly, the multiples of -6 are the same as the multiples of 6.

-6 × 1 = -6; -6 × 2 = -12; -6 × 3 = -18; -6 × 0 = 0; -6 × -1 = 6, -6 × -2 = 12,….

So the multiples of -6 are 0, ±6, ±12, ±18, ±24….etc.

We can see that the multiples of a number are infinite.

More examples,

  • 12 is a multiple of 3 because 3 × 4 = 12
  • 1.2 is a multiple of 0.4, because 0.4 × 3 = 1.2
  • ?6 is a multiple of 3 because 3 × ?2 = ?6
  • -4? is a multiple of ? because ? × (-4) = -4?
  • 7 is NOT a multiple of 3

Note that we must multiply by an integer, but the number that is being multiplied can be anything.

The question can also ask you whether a number is a multiple of another number.

For example, is 42 a multiple of 7?

42 is a multiple of 7 because 7 × 6 = 42

An alternate way to do this is by dividing 42 ÷ 7. If the result of the division is an integer, then the answer is yes.

42 ÷ 7 = 6 (an integer), hence 42 is a multiple of 7.

 

Is 27 a multiple of 81?

  • Yes
  • No

Is 27 a multiple of 81 is the same as saying: Is 27 ÷ 81 = an integer?

27 ÷ 81 = 1/3

Since the result of the division is a non-integer, therefore 27 is not a multiple of 81.

 

Is -20 a multiple of -10?

  • Yes
  • No

Is ?20 a multiple of ?10 is the same as saying: Is ?20 ÷ ?10 = an integer?

?20 ÷ ?10 = 2

Since the result of the division is an integer, therefore ?20 is a multiple of ?10.

 

Is 0.5 a multiple of 0.025?

  • Yes
  • No

Is 0.5 a multiple of 0.025 is the same as saying: Is 0.5 ÷ 0.025 = an integer?

0.5 ÷ 0.025 = 20

Since the result of the division is an integer, therefore 0.5 is a multiple of 0.025.

 

In summary:

  • To find the multiples of any number, multiply that number by an integer.
  • To check whether x is a multiple of y, divide x ÷ y. If the result is an integer, then x is a multiple of y.

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