What is gcd 36,72,90 ?

The solution to gcd 36,72,90 is 18

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Find the GCF 36 , 72 , 90

gcf

36, 72, 90

18

Solution steps

36, 72, 90

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

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

Prime factorization of

90 : 2 \cdot 3 \cdot 3 \cdot 5

90

90

divides by

290 = 45 \cdot 2

= 2 \cdot 45

45

divides by

345 = 15 \cdot 3

= 2 \cdot 3 \cdot 15

15

divides by

315 = 5 \cdot 3

= 2 \cdot 3 \cdot 3 \cdot 5

2, 3, 5

are all prime numbers, therefore no further factorization is possible

= 2 \cdot 3 \cdot 3 \cdot 5

The prime factors common to

36, 72, 90

are

= 2 \cdot 3 \cdot 3

Multiply the numbers:

2 \cdot 3 \cdot 3 = 18

= 18

20 \frac{3}{4} / (1/6)

\frac{31}{9}

(1/2) /8

2.625

1.75 \cdot 1.75