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multiPles

Let us write the factors of 18.

18 = 1 × 18, 18 = 2 × 9 and 18 = 3 × 6
Therefore, 1, 2, 3, 6, 9 and 18 are the factors of 18.

We can say that 18 is a multiple of each of its factors (1, 2, 3, 6, 9 and 18).
Thus, a number is a multiple of each of its factors.
We can define it as “A multiple of a number is obtained by multiplying it with a natural
number (except zero).”

For example, let us multiply 4 by 1, 2, 3, 4, …, we get Knowledge Desk

4 × 1 = 4, 4 × 2 = 8, 4 × 3 = 12, 4 × 4 = 16, … Counting numbers 1,
Here, we get 4, 8, 12, 16, 20, … as the multiples of 4. 2, 3, 4, 5, … are called
example 1: Find the first four multiples of 5. Natural numbers.

Solution: We know that, 5 × 1 = 5, 5 × 2 = 10, 5 × 3 = 15 and 5 × 4 = 20.
Thus, the first four multiples of 5 are 5, 10, 15 and 20.

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example 2: Find the 13 multiple of 12.
Solution: We know that, 13 × 12 = 156.

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Thus, the 13 multiple of 12 is 156. 2 4
example 3: Is 435 a multiple of 18? 18 – 4 3 5
3 6
Solution: If 435 is a multiple of 18, then it should be completely divisible by 18. 7 5
Here, remainder is 3, so 435 is not completely divisible by 18. – 7 2
Hence, 435 is not a multiple of 18. 3

Quick Check

Match the column I with the column II.
Column I Column II
(a) 18 (i) multiple of 24
(b) 49 (ii) greatest factor of 18

(c) 1 (iii) multiple of 7
(d) 3 (iv) smallest factor of any numbers
(e) 48 (v) a factor of 12

Properties of multiples

1. Every number is a multiple of itself.
examples: 2 = 2 × 1, 8 = 8 × 1, 24 = 24 × 1, etc.

2. Every number is a multiple of 1.
examples: 5 = 1 × 5, 15 = 1 × 15, 100 × 1 = 100, etc.

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