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Find the GCF 30 , 48

Solution

gcf

30, 48

6

Solution steps

30, 48

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

48 : 2 \cdot 2 \cdot 2 \cdot 2 \cdot 3

48

48

divides by

248 = 24 \cdot 2

= 2 \cdot 24

24

divides by

224 = 12 \cdot 2

= 2 \cdot 2 \cdot 12

12

divides by

212 = 6 \cdot 2

= 2 \cdot 2 \cdot 2 \cdot 6

6

divides by

26 = 3 \cdot 2

= 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 3

The prime factors common to

30, 48

are

= 2 \cdot 3

Multiply the numbers:

2 \cdot 3 = 6

= 6

1 \frac{6}{18} / (5/6)

(21/1) /1 \frac{3}{4}

\frac{22}{3}

6.375

\frac{108}{8}