What is gcd 180,315 ?

The solution to gcd 180,315 is 45

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Find the GCF 180 315

gcf

180, 315

45

Solution steps

180, 315

Prime factorization of

180 : 2 \cdot 2 \cdot 3 \cdot 3 \cdot 5

180

180

divides by

2180 = 90 \cdot 2

= 2 \cdot 90

90

divides by

290 = 45 \cdot 2

= 2 \cdot 2 \cdot 45

45

divides by

345 = 15 \cdot 3

= 2 \cdot 2 \cdot 3 \cdot 15

15

divides by

315 = 5 \cdot 3

= 2 \cdot 2 \cdot 3 \cdot 3 \cdot 5

2, 3, 5

are all prime numbers, therefore no further factorization is possible

= 2 \cdot 2 \cdot 3 \cdot 3 \cdot 5

Prime factorization of

315 : 3 \cdot 3 \cdot 5 \cdot 7

315

315

divides by

3315 = 105 \cdot 3

= 3 \cdot 105

105

divides by

3105 = 35 \cdot 3

= 3 \cdot 3 \cdot 35

35

divides by

535 = 7 \cdot 5

= 3 \cdot 3 \cdot 5 \cdot 7

3, 5, 7

are all prime numbers, therefore no further factorization is possible

= 3 \cdot 3 \cdot 5 \cdot 7

The prime factors common to

180, 315

are

= 3 \cdot 3 \cdot 5

Multiply the numbers:

3 \cdot 3 \cdot 5 = 45

= 45

48, 72, 96

\frac{29}{7}

0.81

180 - 66

\frac{3}{10}