# Solutions to Questions on Greatest Common Factor (GCF)

Detailed solutions of questions on greatest common factor are presented.

A
Greatest Factor Calculator (GCF) may be used to check your answers.

Find the greatest common factor of 36 and 42.

__Solution__

The prime factorization of 36 and 42 are:

36 = 2 × 2 × 3 × 3

42 = 2 × 3 × 7

GCF of 36 and 42 = 2 × 3 = 6

Find the greatest common factor of 45, 60 and 75.

__Solution__

The prime factorization of 45, 60 and 75 are:

45 = 3 × 3 × 5

60 = 2 × 2 × 3 × 5

75 = 3 × 5 × 5

GCF of 45, 60 and 75 = 3 × 5 = 15

What is the greatest common factor of of 360 and 252?

__Solution__

The prime factorization of 360 and 252 are:

360 = 2 × 2 × 2 × 3 × 3 × 5

252 = 2 × 2 × 3 × 3 × 7

GCF of 360 and 252 = 2 × 2 × 3 × 3 = 36

What is the greatest common factor of 324, 666 and 756?

__Solution__

The prime factorization of 324, 666 and 756 are:

324 = 2 × 2 × 3 × 3 × 3 × 3

666 = 2 × 3 × 3 × 37

756 = 2 × 2 × 3 × 3 × 3 × 7

GCF of 324, 666 and 756 = 2 × 3 × 3 = 18

a) Find the GCF of 12 and 16.

b) Use the result in part a) to find the GCF of 1200 and 1600.

__Solution__

a) The prime factorization of 12 and 16 are:

12 = 2× 2 × 3

16 = 2 × 2 × 2 × 2

GCF of 12 and 16 = 2 × 2 = 4

b) We first note that

1200 = 12 × 100 = 2 × 2 × 3 × 100

1600 = 16 × 100 = 2 × 2 × 2 × 2 × 100

and so the greatest common factor to 1200 and 1600 is given by

2× 2 × 100 = 400

## Links and References

Middle School Math (Grades 6, 7, 8, 9) - Free Questions and Problems With Answers

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