The solution to gcd 36,54 is 18

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Find the GCF 36 , 54

Solution

gcf

36, 54

18

Solution steps

36, 54

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

54 : 2 \cdot 3 \cdot 3 \cdot 3

54

54

divides by

254 = 27 \cdot 2

= 2 \cdot 27

27

divides by

327 = 9 \cdot 3

= 2 \cdot 3 \cdot 9

9

divides by

39 = 3 \cdot 3

= 2 \cdot 3 \cdot 3 \cdot 3

2, 3

are all prime numbers, therefore no further factorization is possible

= 2 \cdot 3 \cdot 3 \cdot 3

The prime factors common to

36, 54

are

= 2 \cdot 3 \cdot 3

Multiply the numbers:

2 \cdot 3 \cdot 3 = 18

= 18

3.48

\frac{16}{12}

t h e \frac{54}{90}

36, 90

3.16