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.

1. 
   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
   
2. 
   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
   
3. 
   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
   
4. 
   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
   
5. 
   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
   

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