Page 53 - ICSE Math 6

To find all the factors of a number, write it as a product of two numbers in all possible ways. Then
each number in a product is a factor of the given number.

Properties of factors
• 1 is a factor of every number.
• Every number is a factor of itself.

• A factor of a number is an exact divisor of that number.
• A factor of a number is either less than or equal to the given number.

• Factors of a number are finite.

Example 2: Find all the factors of 18.
Solution: Write 18 as a product of two numbers in all possible ways.

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

(a) 15 is a factor of 315 (b) 21 is a factor of 188

Solution: (a) Let’s divide 315 by 15. (b) Let’s divide 188 by 21.
21 8
15 315 21 188
–30 –168
15 20
–15 As 21 does not divide 188 completely,
× therefore 21 is not a factor of 188.

As 15 divides 315 completely,
therefore 15 is a factor of 315.

Multiples

A multiple of a number is obtained by multiplying the given number by a natural number. For example,
multiples of 7 are 7, 14, 21, … which are obtained by 7 × 1 = 7, 7 × 2 = 14, 7 × 3 = 21, …
As every number can be multiplied by infinite natural numbers therefore there are infinite multiples
of a number.

Properties of multiples

• A multiple of a number is greater than or equal to the number.
• Every number is a multiple of 1 and itself.

• Multiples of a number are infinite.

Example 4: Find all the multiples of 13 up to 100.

Solution: Multiples of 13 up to 100 are:
13 × 1 = 13 13 × 2 = 26 13 × 3 = 39 13 × 4 = 52
13 × 5 = 65 13 × 6 = 78 13 × 7 = 91

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