Properties of Multiples

The properties of multiples are discussed step-by-step according to its property.


Property (1):

Every number is a multiple of 1.

As: 7 x 1 = 7,

9 x 1 = 9, 

15 x 1 = 15, 

40 x 1 = 40

Property (2):

Every number is the multiple of itself.

As: 1 x 7 = 7, 

1 x 21 = 21,

1 x 105 = 105,

1 x 212 = 212

For example, 8 × 1 = 8. Hence, 8 is multiple of itself. 19 × 1 = 19. So, 19 is multiple of itself.


Property (3):

Zero (0) is a multiple of every number.


As: 0 x 9 = 0,

0 x 11 = 0,

0 x 57 = 0,

0 x 275 = 0


Property (4):

Every multiple except zero is either equal to or greater than any of its factors.


As, multiple of 7 = 7, 14, 28, 35, 77, …………., etc.

For example, multiples of 4 are 4, 8, 12, 16. We find that every multiple of 4 is either greater or equal to 4.


Property (5):

The product of two or more factors is the multiple of each factor.


As: 3 x 7 = 21,

So, 21 is the multiple of both 3 and 7.

30 = 2 x 3 x 5,

So, 30 is the multiple of 2, 3 and 5.

For example, the product of 3 × 4 × 5 is 60 and 60 is also a multiple of 3, 4 and 5.


Property (6):

There is no end to multiples of a number.


As: 5, 10, 15, 20, 25, …………….., 100, 105, 110, …………………., are the multiples of 5.


These are the properties of multiples.


Explain the Properties of Multiples step-by-step with examples.

Observe the following:

12 × 1 = 12;

18 × 1 = 18;

25 × 1 = 25;


12 × 1 = 12 implies 12 is of 12 and 12 is a multiple of 1.

18 × 1 = 18 implies 18 is a multiple of 18 and 18 is a multiple of 1.

25 × 1 = 25 implies 25 is a multiple of 25 and 25 is a multiple of 1.


What do we conclude?

We conclude,

Every number is a multiple of itself.

Every number is a multiple of 1.


Again, observe the following:

Multiples of 5 are 5, 10, 15, 20, ...

Multiple of 12 are 12, 24, 36, 48, ...

Multiple of 18 are 18, 36, 54, 72, ...


What do we observe?

We see that every multiple of 5 is either greater than or equal to 5.

Similarly, every multiple of 12 is either greater than or equal to 12.

Every multiple of 18 is either greater than or equal to 18.


Hence, we can say that

Every multiple of a number is either greater than or equal to the number.

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