What is gcd 75,105,135,165 ?

The solution to gcd 75,105,135,165 is 15

gcd 75,105,135,165

gcd

15

Solution steps

75, 105, 135, 165

Prime factorization of

75 : 3 \cdot 5 \cdot 5

75

75

divides by

375 = 25 \cdot 3

= 3 \cdot 25

25

divides by

525 = 5 \cdot 5

= 3 \cdot 5 \cdot 5

3, 5

are all prime numbers, therefore no further factorization is possible

= 3 \cdot 5 \cdot 5

Prime factorization of

105 : 3 \cdot 5 \cdot 7

105

105

divides by

3105 = 35 \cdot 3

= 3 \cdot 35

35

divides by

535 = 7 \cdot 5

= 3 \cdot 5 \cdot 7

3, 5, 7

are all prime numbers, therefore no further factorization is possible

= 3 \cdot 5 \cdot 7

Prime factorization of

135 : 3 \cdot 3 \cdot 3 \cdot 5

135

135

divides by

3135 = 45 \cdot 3

= 3 \cdot 45

45

divides by

345 = 15 \cdot 3

= 3 \cdot 3 \cdot 15

15

divides by

315 = 5 \cdot 3

= 3 \cdot 3 \cdot 3 \cdot 5

3, 5

are all prime numbers, therefore no further factorization is possible

= 3 \cdot 3 \cdot 3 \cdot 5

Prime factorization of

165 : 3 \cdot 5 \cdot 11

165

165

divides by

3165 = 55 \cdot 3

= 3 \cdot 55

55

divides by

555 = 11 \cdot 5

= 3 \cdot 5 \cdot 11

3, 5, 11

are all prime numbers, therefore no further factorization is possible

= 3 \cdot 5 \cdot 11

The prime factors common to

75, 105, 135, 165

are

= 3 \cdot 5

Multiply the numbers:

3 \cdot 5 = 15

= 15