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.
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Is 27 a multiple of 81?
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. |
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Is -20 a multiple of -10?
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. |
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Is 0.5 a multiple of 0.025?
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.