GCF (HCF) of 84 and 112

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What is the Greatest Common Divisor of 84 and 112?

Answer

GCF (HCF) of 84 and 112 is
28

Common factors: 1, 2, 4, 7, 14, 28

28 divides both: 84 ÷ 28 = 3, 112 ÷ 28 = 4 — and 3 and 4 share no factor but 1, so no larger number divides both.

84 = 22 × 3 × 7

112 = 24 × 7

Prime84112Lowest power
2222422
33——
7777

— = power 0: the prime is not a factor of this number, so it cannot be in the GCF.

GCF = 22 × 7 = 28

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GCF Table

Number 1Number 2GCF
84971
849814
84993
841004
841011
841026
841031
841044
8410521
841062
841071
8410812
841091
841102
841113
8411228
841131
841146
841151
841164
841173
841182
841197
8412012
841211
841222
841233
841244
841251
8412642

FAQ

What is the Greatest Common Divisor of 84 and 112?

GCF (HCF) of 84 and 112 is 28

How to find the GCF of 84 and 112?

You can find the GCF of 84 and 112 by listing all factors of both numbers and picking the greatest common one, or by prime factorization. The GCF of 84 and 112 is 28.

What prime factors do 84 and 112 share?

The prime factorizations of 84 and 112 have 2 × 2 × 7 in common, and multiplying those shared primes gives 28 — exactly the greatest common factor.

How does the GCF reduce the fraction 84/112?

Divide the numerator and the denominator by the GCF 28: 84 ÷ 28 = 3 and 112 ÷ 28 = 4. So 84/112 in lowest terms is 3/4.

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