Page 58 - ICSE Math 6

11. Write a digit in the blank space of each of the following numbers so that the number formed is
divisible by 9.
(a) 24,1__,279 (b) 5,94,__84
12. Write a digit in the blank space of each of the following numbers so that the number formed is
divisible by 11.
(a) 9,32,__38 (b) 8,__9,487

Common Factors

A number which exactly divides two or more given numbers is the common factor of the given
numbers. For example, let’s find the common factors of 15 and 18.
The factors of 15 are 1 , 3 , 5 and 15.

The factors of 18 are 1 , 2, 3 , 6, 9 and 18.
Therefore, the common factors of 15 and 18 are 1 and 3.

Common Multiples

A number which is exactly divisible by two or more given numbers is the common multiple of the
given numbers. For example, let’s find the common multiples of 15 and 18.
Multiples of 15 are 15, 30, 45, 60, 75, 90 , 105, 120, 135, 150, 165, 180 and so on.

Multiples of 18 are 18, 36, 54, 72, 90 , 108, 126, 144, 162, 180 and so on.
Therefore, the common multiples of 15 and 18 are 90, 180 and so on.

Co-prime Numbers
Two numbers having only 1 as the common factor are called co-prime numbers. For example, 7 and
11 are co-prime numbers as 1 is the only common factor of both 7 and 11.

• A pair of prime numbers is always co-prime.

• A pair of composite numbers can also be co-prime numbers.

Example 12: Find the common factors of:
(a) 30 and 64 (b) 56 and 120
Solution: (a) All possible factors of 30 are 1, 2, 3, 5, 6, 10, 15 and 30.
All possible factors of 64 are 1, 2, 4, 8, 16, 32 and 64.

Therefore, common factors of 30 and 64 are 1 and 2.
(b) All possible factors of 56 are 1, 2, 4, 7, 8, 14, 28 and 56.
All possible factors of 120 are 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60 and
120.
Therefore, common factors of 56 and 120 are 1, 2, 4 and 8.

Example 13: Find the first three common multiples of: (a) 4 and 6 (b) 12 and 18
Solution: (a) Multiples of 4 are 4, 8, 12, 16, 20, 24, 28, 32, 36, ...

Multiples of 6 are 6, 12, 18, 24, 30, 36, ...
First three common multiples of 4 and 6 are 12, 24 and 36.

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