Page 62 - ICSE Math 5

F
5 Factors and Multiplesactors and Multiples

Learning Outcomes

Students will be able to learn:
 to find factors and common factors of the given numbers.
 to find prime factors of a number by factor tree method and prime factorization method.
 to find multiples and common multiples of given numbers.
 about prime numbers, composite numbers, twin prime numbers and co-prime numbers.
 the tests of divisibility of numbers by 2, 3, 4, 5, 6, 8, 9, 10 and 11.
 to find Highest Common Factor (H.C.F.) by listing method and common division method.
 to find Least Common Multiple (L.C.M.) by listing method and common division method.
 the relationship between H.C.F. and L.C.M. of two numbers.

Factors

We have already learnt in the previous class that factors are the numbers that can be multiplied
together to get a product. In other words, factors of a given number divides the number completely
without leaving any remainder.

For example, 12 × 18 = 216 where 12 and 18 are the factors of 216.
When we divide 216 by 12 and 18 separately, we get 216  12 = 18 and 216  18 = 12. Thus, we
can say that the factors of 216 divide it completely without leaving any remainder.
Example 1: Find any five factors of 36 and 225.

Solution: Five factors of 36 are 1, 2, 3, 4 and 6.

Five factors of 225 are 1, 3, 5, 15 and 45.
Common factors are the factors that are common to the given numbers.
To find the common factors of two or more numbers, we find the factors of each number, and
then compare and identify the common factors among them.
Example 2: Find the common factors of 22 and 24.

Solution: Factors of 22 are 1, 2, 11 and 22 because 1 × 22 = 22 and 2 × 11 = 22.
Factors of 24 are 1, 2, 3, 4, 6, 8, 12 and 24 because 1 × 24 = 24, 2 × 12 = 24,
3 × 8 = 24 and 4 × 6 = 24.

So, the common factors of 22 and 24 are 1 and 2.
Example 3: Determine whether 14 is a factor of 56 or not. 4
Solution: Divide the larger number by the smaller number, 56  14. 14 5 6

If the remainder is 0 on dividing, then the smaller number is the – 5 6
factor of the larger number. 0 0
Since, 56  14 = 4 and there is no remainder left, therefore 14 is a factor of 56.

52