Page 78 - ICSE Math 4

Try 5  5 × ? = 24 (Not possible)
Try 6  6 × 4 = 24 (We will stop here since from now on the factors
are repea ng.)

Step 2: Write all the factors of the given number.

So, 1, 2, 3, 4, 6, 8, 12 and 24 are the factors of 24.

Factors of 24 by division

Step 1: Divide the given number by a divisor that gives 0 as remainder.
Try 1  24 ÷ 1 = 24 (quo ent = 24 and remainder = 0)

Try 2  24 ÷ 2 = 12 (quo ent = 12 and remainder = 0)

Try 3  24 ÷ 3 = 8 (quo ent = 8 and remainder = 0)

Try 4  24 ÷ 4 = 6 (quo ent = 6 and remainder = 0)

Try 5  24 ÷ 5 = ? (not possible)
Try 6  24 ÷ 6 = 4 (quo ent = 4 and remainder = 0)

We will stop here since division of 24 by any other number is not
possible.

Step 2: Write the divisor and quo ent of the given number as the factors of 24.

So, 1, 2, 3, 4, 6, 8, 12 and 24 are the factors of 24.

Properties of Factors

• 1 is a factor of every number and is the smallest factor of that number.
For example, 1 × 4 = 4; 1 × 6 = 6; and 1 × 25 = 25, where 1 is the factor of every
number.

• 1 is the only number that has only one factor.

For example, 1 × 1 = 1.

• Every number is a factor of itself and is the greatest factor of that number.

For example, let’s fi nd the factors of 12: 1 × 12 = 12; 2 × 6 = 12; and 3 × 4 = 12, where
1, 2, 3, 4, 6 and 12 are the factors of 12. It can be seen that 12 is the greatest factor
of itself.

• There are fi nite (limited) number of factors for a given number.

For example, 12 has only 6 factors, i.e., 1, 2, 3, 4, 6 and 12.
• Factors of a given number are always smaller than or equal to that number.

For example, the factors of 15 are 1, 3, 5 and 15 which are either smaller than or

equal to 15.

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