Examples of Greatest Common Factor (G.C.F)

G.C. F (Greatest Common Factor) is same as Highest Common Factor (H.C. F) that is the highest or greatest number by which two or more number is completely divisible without leaving any remainder.

This topic on G.C. F (Greatest Common Factor) will provide a wide range of examples which would be helpful to the learners for their better understanding and knowledge.

Here examples on G.C. F (Greatest Common Factor) are illustrated below:

1. Find the greatest common factor of 77 and 84

Solution:

The prime factors of 77 are= 7 × 11 

The prime factors of 84 are: 2 × 2 × 3 × 7 = 2² × 3 × 7

The common prime factor of 77 and 84 is 7

The lowest power of 7 is 7

Therefore, G. C. F = 7

2. Find the greatest common factor of 92 and 230

Solution:

The prime factors of 92 are: 2 × 2 × 23 = 2² × 23

The prime factors of 230 are: 2 × 5 × 23

The common prime factors of 92 and 230 are 2 and 23

The lowest power of 2 is 2

The lowest power of 23 is 23

Therefore, G. C. F = 2 × 23 = 46

3. Find the greatest common factor of 120, 240, and 360

Solution:

The prime factors of 120 are: 2 × 2 × 2 × 3 × 5 = 2³ × 3 × 5

The prime factors of 240 are: 2 × 2 × 2 × 2 × 3 × 5 = 2⁴ × 3 × 5

The prime factors of 240 are: 2 × 2 × 2 × 3 × 3 × 5 = 2³ × 3² ×5

The common prime factors of 120, 240 and 360 are 2, 3, 5

The lowest power of 2 is 2³

The lowest power of 3 is 3

The lowest power of 5 is 5

Therefore, G. C. F = 2³ × 3 × 5 = 2 × 2 × 2 × 3 × 5 = 120

4. Find the greatest common factor of 48 and 96

Solution:

The prime factors of 48 are: 2 × 2 × 2 × 2 × 3 = 2⁴ × 3

The prime factors of 96 are: 2 × 2 × 2 × 2 × 2 × 3 = 2⁵ × 3

The common prime factors of 48 and 96 are 2 and 3

The lowest power of 2 is 2⁴

The lowest power of 3 is 3

Therefore, G. C. F = 2⁴ × 3 = 2 × 2 × 2 × 2 × 3 = 48

5. Find the greatest common factor of 255, 170 and 85

Solution:

The prime factors of 255 are: 5 × 3 × 17

The prime factors of 170 are: 2 × 5 × 17

The prime factors of 85 are: 5 × 17

The common prime factors of 255, 170 and 85 are 5 and 17

The lowest power of 5 is 5

The lowest power of 17 is 17

Therefore, G. C. F = 5 × 17 = 85

5th Grade Math

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