The solution to gcd 28,42 is 14

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Find the GCF 28 and 42

Solution

gcf

28, 42

14

Solution steps

28, 42

Prime factorization of

28 : 2 \cdot 2 \cdot 7

28

28

divides by

228 = 14 \cdot 2

= 2 \cdot 14

14

divides by

214 = 7 \cdot 2

= 2 \cdot 2 \cdot 7

2, 7

are all prime numbers, therefore no further factorization is possible

= 2 \cdot 2 \cdot 7

Prime factorization of

42 : 2 \cdot 3 \cdot 7

42

42

divides by

242 = 21 \cdot 2

= 2 \cdot 21

21

divides by

321 = 7 \cdot 3

= 2 \cdot 3 \cdot 7

2, 3, 7

are all prime numbers, therefore no further factorization is possible

= 2 \cdot 3 \cdot 7

The prime factors common to

28, 42

are

= 2 \cdot 7

Multiply the numbers:

2 \cdot 7 = 14

= 14

\frac{14}{3}

\frac{78}{3}

\frac{55}{4}

4 \frac{1}{5}

147