What is gcd 56,84,112 ?

The solution to gcd 56,84,112 is 28

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gcd 56,84,112

gcf

56, 84, 112

28

Solution steps

56, 84, 112

Prime factorization of

56 : 2 \cdot 2 \cdot 2 \cdot 7

56

56

divides by

256 = 28 \cdot 2

= 2 \cdot 28

28

divides by

228 = 14 \cdot 2

= 2 \cdot 2 \cdot 14

14

divides by

214 = 7 \cdot 2

= 2 \cdot 2 \cdot 2 \cdot 7

2, 7

are all prime numbers, therefore no further factorization is possible

= 2 \cdot 2 \cdot 2 \cdot 7

Prime factorization of

84 : 2 \cdot 2 \cdot 3 \cdot 7

84

84

divides by

284 = 42 \cdot 2

= 2 \cdot 42

42

divides by

242 = 21 \cdot 2

= 2 \cdot 2 \cdot 21

21

divides by

321 = 7 \cdot 3

= 2 \cdot 2 \cdot 3 \cdot 7

2, 3, 7

are all prime numbers, therefore no further factorization is possible

= 2 \cdot 2 \cdot 3 \cdot 7

Prime factorization of

112 : 2 \cdot 2 \cdot 2 \cdot 2 \cdot 7

112

112

divides by

2112 = 56 \cdot 2

= 2 \cdot 56

56

divides by

256 = 28 \cdot 2

= 2 \cdot 2 \cdot 28

28

divides by

228 = 14 \cdot 2

= 2 \cdot 2 \cdot 2 \cdot 14

14

divides by

214 = 7 \cdot 2

= 2 \cdot 2 \cdot 2 \cdot 2 \cdot 7

2, 7

are all prime numbers, therefore no further factorization is possible

= 2 \cdot 2 \cdot 2 \cdot 2 \cdot 7

The prime factors common to

56, 84, 112

are

= 2 \cdot 2 \cdot 7

Multiply the numbers:

2 \cdot 2 \cdot 7 = 28

= 28

(- 1)^{2} - 4

2 - (3 + 2)^{2} + 2 (3)

\frac{8}{4} (2 + 2)

3 \cdot 3 \cdot 3 \cdot 3

17 + (- 8) + (- 8)