I need to find the number used to divide

Question

Kono divides the numerator and denominator of 48 over 72 by the greatest common factor to simplify the fraction in one step. By what number does he divide?

Answer 1

48/72

 

Take the numbers and break them down to prime factors

         48                         72

       2   24                    2   36

      2  2  12                2   2  18

     2  2  2  6              2   2   2  9

   2  2   2  2  3         2   2   2  3   3

 

The common terms are 2*2*2*3 = 24 for the GCF

 

48/72 = [24(2)]/[24(3)] = 2/3

  

Answer 2

Greatest common factor....

 

Using factor trees:     48 = 8 x 6 = 2 x 2 x2 x 2 x3

                               72 = 8 x 9 =  2 x2 x2 x 3 x 3

 

   The prime factors in common are 2 x 2 x 2 x 3 = 24.

 

   So dividing by 24/24 results is 48/72 divided by 24/24 = 2/3

 

 

Using Euclid's Method:

 

    72 divided by 48 = 1 remainder 24

   48 divided by 24 = 2 remainder 0 <--- remainder is zero! can stop here!  the last number divided by is 24.

 

The GCF is 24. 

Dividing the top of 48 and the bottom of 72 BOTH by 24 reduces 48/72 to 2/3 in lowest terms in one step.

 

Definition of Greatest Common Factor is in fact the Largest number that divides the top and bottom

evenly, so that the fraction is reduces to lowest terms in one single step.

 

The two methods for finding the GCF, as shown, are prime factor trees and Euclid's Method