Page 77 - ICSE Math 4

Factors and Multiplesactors and Multiples
7 F

Learning Outcomes

Students will be able to learn:
 about factors and multiples of a number.
 about prime and composite numbers.
 to fi nd prime factors of a number by factor tree method and prime factorization
method.
 about tests of divisibility of numbers by 2, 3, 4, 5, 9 and 10.
 to fi nd Highest Common Factor (H.C.F.) by listing and common division methods.
 to fi nd Least Common Multiple (L.C.M.) by listing and common division methods.

Factors of a Number Top Tip

We have already learnt mul plica on of numbers in We can always write a

which two numbers are mul plied to get the product. number as the product of
its factors.
The numbers that we mul ply together to get a product
For example, 12 = 4 × 3.
are called factors.
Let’s consider a number 16 and fi nd out its factors.

We have, 1 × 16 = 16, 2 × 8 = 16 and 4 × 4 = 16. Here, 1, 2, 4, 8 and 16 are the factors
of 16.

The factor of any number is a divisor that divides the number completely without leaving
a remainder.

For example, when 16 is divided by 1, 2, 4, 8 and 16 separately, the remainder is 0.

Thus, we can say that both the divisor and the quo ent are the factors of the dividend,
when the remainder is 0.

So, we can fi nd the factors of a number by either mul plica on or division.
Example 1: Write all the factors of 24.

Solu on: Factors of 24 by mul plica on

Step 1: Find out the numbers that can be mul plied to get the given number.

Try 1  1 × 24 = 24 (1 and 24 are factors of 24.)
Try 2  2 × 12 = 24 (2 and 12 are factors of 24.)

Try 3  3 × 8 = 24 (3 and 8 are factors of 24.)

Try 4  4 × 6 = 24 (4 and 6 are factors of 24.)

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