What is gcd 60,72,96,120 ?

The solution to gcd 60,72,96,120 is 12

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Popular Pre Algebra >

gcd 60,72,96,120

Solution

gcd

Solution

12

Solution steps

60, 72, 96, 120

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

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

96 : 2 \cdot 2 \cdot 2 \cdot 2 \cdot 2 \cdot 3

96

96

divides by

296 = 48 \cdot 2

= 2 \cdot 48

48

divides by

248 = 24 \cdot 2

= 2 \cdot 2 \cdot 24

24

divides by

224 = 12 \cdot 2

= 2 \cdot 2 \cdot 2 \cdot 12

12

divides by

212 = 6 \cdot 2

= 2 \cdot 2 \cdot 2 \cdot 2 \cdot 6

6

divides by

26 = 3 \cdot 2

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

2, 3

are all prime numbers, therefore no further factorization is possible

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

Prime factorization of

120 : 2 \cdot 2 \cdot 2 \cdot 3 \cdot 5

120

120

divides by

2120 = 60 \cdot 2

= 2 \cdot 60

60

divides by

260 = 30 \cdot 2

= 2 \cdot 2 \cdot 30

30

divides by

230 = 15 \cdot 2

= 2 \cdot 2 \cdot 2 \cdot 15

15

divides by

315 = 5 \cdot 3

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

2, 3, 5

are all prime numbers, therefore no further factorization is possible

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

The prime factors common to

60, 72, 96, 120

are

= 2 \cdot 2 \cdot 3

Multiply the numbers:

2 \cdot 2 \cdot 3 = 12

= 12

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Frequently Asked Questions (FAQ)

What is gcd 60,72,96,120 ?
The solution to gcd 60,72,96,120 is 12

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