Playing with Numbers

A **factor** of a number is an exact divisor of that number.

Example: 3 is an exact divisor of 15 (15 = 3 × 5). So, 3 is a factor of 15.

2 is not an exact factor of 17 (since any whole number multiplied with 2 does not give 17). So, 2 is not a factor of 17.

We can find the multiples of a given number by multiplying 1, 2, 3 …, to the number.

Example: To find the multiples of 12, we need to calculate as follows:

12 × 1 = 12, 12 × 2 = 24, 12 × 3 = 36, 12 × 4 = 48 …, and so on.

So, the numbers 12, 24, 36, 48, etc., are the multiples of 12.

**Properties of natural numbers with respect to their factors:**- 1 is a factor of every number. For example, 5 = 1 × 5, 19 = 1 × 19

- Every number is a factor of itself. For example, 20 = 20 × 1. This shows that 20 is a factor of 20.
- Every factor of a number is less than or equal to the number. For example, factors of 12 are 1, 2, 3, 4, 6 and 12. Here, 1, 2, 3, 4, 6 and 12 are less than or equal to 12.
- Every number has finite factors. For example, the factors of 30 are 1, 2, 3, 5, 6, 10, 15 and 30. Here, we may observe that there are only 8 factors of 30.

**Properties of natural numbers with respect to their multiples:**- Every number is a multiple of itself. For example, 15 × 1 = 15, 7 × 1 = 7
- Every multiple of a number is greater than or equal to that number.For example, the multiple of 6 is 6, 12, 18 … Here we may observe th…

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