The solution to gcd 36,60 is 12

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Find the GCF 36 , 60

Solution

gcf

36, 60

12

Solution steps

36, 60

Prime factorization of

36 : 2 \cdot 2 \cdot 3 \cdot 3

36

36

divides by

236 = 18 \cdot 2

= 2 \cdot 18

18

divides by

218 = 9 \cdot 2

= 2 \cdot 2 \cdot 9

9

divides by

39 = 3 \cdot 3

= 2 \cdot 2 \cdot 3 \cdot 3

2, 3

are all prime numbers, therefore no further factorization is possible

= 2 \cdot 2 \cdot 3 \cdot 3

Prime factorization of

60 : 2 \cdot 2 \cdot 3 \cdot 5

60

60

divides by

260 = 30 \cdot 2

= 2 \cdot 30

30

divides by

230 = 15 \cdot 2

= 2 \cdot 2 \cdot 15

15

divides by

315 = 5 \cdot 3

= 2 \cdot 2 \cdot 3 \cdot 5

2, 3, 5

are all prime numbers, therefore no further factorization is possible

= 2 \cdot 2 \cdot 3 \cdot 5

The prime factors common to

36, 60

are

= 2 \cdot 2 \cdot 3

Multiply the numbers:

2 \cdot 2 \cdot 3 = 12

= 12

\frac{4}{3}

4.25

t o a p erce n t a g e 12/13

\frac{18}{7}

t o a p erce n t a g e 8/12