The solution to gcd 108,72 is 36

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Find the GCF 108 , 72

Solution

gcf

108, 72

36

Solution steps

108, 72

Prime factorization of

108 : 2 \cdot 2 \cdot 3 \cdot 3 \cdot 3

108

108

divides by

2108 = 54 \cdot 2

= 2 \cdot 54

54

divides by

254 = 27 \cdot 2

= 2 \cdot 2 \cdot 27

27

divides by

327 = 9 \cdot 3

= 2 \cdot 2 \cdot 3 \cdot 9

9

divides by

39 = 3 \cdot 3

= 2 \cdot 2 \cdot 3 \cdot 3 \cdot 3

2, 3

are all prime numbers, therefore no further factorization is possible

= 2 \cdot 2 \cdot 3 \cdot 3 \cdot 3

Prime factorization of

72 : 2 \cdot 2 \cdot 2 \cdot 3 \cdot 3

72

72

divides by

272 = 36 \cdot 2

= 2 \cdot 36

36

divides by

236 = 18 \cdot 2

= 2 \cdot 2 \cdot 18

18

divides by

218 = 9 \cdot 2

= 2 \cdot 2 \cdot 2 \cdot 9

9

divides by

39 = 3 \cdot 3

= 2 \cdot 2 \cdot 2 \cdot 3 \cdot 3

2, 3

are all prime numbers, therefore no further factorization is possible

= 2 \cdot 2 \cdot 2 \cdot 3 \cdot 3

The prime factors common to

108, 72

are

= 2 \cdot 2 \cdot 3 \cdot 3

Multiply the numbers:

2 \cdot 2 \cdot 3 \cdot 3 = 36

= 36

\frac{15}{7}

5 \frac{1}{4}

0.6666

(10/13) / (11/13)

t h e \frac{81}{90}