What is gcd 10,12,14 ?

The solution to gcd 10,12,14 is 2

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Find the GCF 10 , 12 , 14

gcf

10, 12, 14

2

Solution steps

10, 12, 14

Prime factorization of

10 : 2 \cdot 5

10

10

divides by

210 = 5 \cdot 2

= 2 \cdot 5

2, 5

are all prime numbers, therefore no further factorization is possible

= 2 \cdot 5

Prime factorization of

12 : 2 \cdot 2 \cdot 3

12

12

divides by

212 = 6 \cdot 2

= 2 \cdot 6

6

divides by

26 = 3 \cdot 2

= 2 \cdot 2 \cdot 3

2, 3

are all prime numbers, therefore no further factorization is possible

= 2 \cdot 2 \cdot 3

Prime factorization of

14 : 2 \cdot 7

14

14

divides by

214 = 7 \cdot 2

= 2 \cdot 7

2, 7

are all prime numbers, therefore no further factorization is possible

= 2 \cdot 7

The prime factors common to

10, 12, 14

are

= 2

\frac{28}{5}

\frac{42}{2}

125 \cdot 4

\frac{4420}{170}

\frac{33}{2}