GREATEST COMMON FACTOR

What is greatest common factor ?

The GCF (greatest common factor) of two or more numbers divides each of the numbers without a remainder.

Properties of greatest common factor :

The GCF of two or more numbers is a factor of each of the numbers.
The GCF of two or more numbers is always less than or equal to each of the numbers.
The GCF of two or more prime numbers is 1 always.

Methods of finding greatest common factor :

Writing the factors of given numbers and selecting the common factors.
Divide the given numbers using prime factorization until we receive numbers which are not divisible by the same times table.

Problem 1 :

(a) List all the factors of 10

(b) List all the factors of 15

Solution :

a) Factors of 10 are

10, 20, 30, 40, 50, 60, 70, 80 ..................

b) Factors of 15 are

15, 30, 45, 60, 75, 90 ...........

c) Common factors of 10 and 15 are

30, 60, 90, .................

Problem 2 :

(a) List all the factors of 12

(b) List all the factors of 18

Solution :

a) Factors of 12 are

12, 24, 36, 48, .................

b) Factors of 18 are

18, 36, 54, 72, .................

c) Common factors for 12 are 18 are

36, 72, 108, ..............

Write down all the common factors of each of these pairs of numbers.

Problem 3 :

6 and 8

Problem 4 :

(b) 15 an

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