What is gcd 30,42,54 ?

The solution to gcd 30,42,54 is 6

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Find the GCF 30 , 42 , 54

gcf

30, 42, 54

6

Solution steps

30, 42, 54

Prime factorization of

30 : 2 \cdot 3 \cdot 5

30

30

divides by

230 = 15 \cdot 2

= 2 \cdot 15

15

divides by

315 = 5 \cdot 3

= 2 \cdot 3 \cdot 5

2, 3, 5

are all prime numbers, therefore no further factorization is possible

= 2 \cdot 3 \cdot 5

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

Prime factorization of

54 : 2 \cdot 3 \cdot 3 \cdot 3

54

54

divides by

254 = 27 \cdot 2

= 2 \cdot 27

27

divides by

327 = 9 \cdot 3

= 2 \cdot 3 \cdot 9

9

divides by

39 = 3 \cdot 3

= 2 \cdot 3 \cdot 3 \cdot 3

2, 3

are all prime numbers, therefore no further factorization is possible

= 2 \cdot 3 \cdot 3 \cdot 3

The prime factors common to

30, 42, 54

are

= 2 \cdot 3

Multiply the numbers:

2 \cdot 3 = 6

= 6

t o a p erce n t a g e 15/16

t o a p erce n t a g e 18/20

\frac{80}{12}

100 - 12

0.6666667