GCF (HCF) of 84 and 120

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What is the Greatest Common Divisor of 84 and 120?

Answer

GCF (HCF) of 84 and 120 is
12

Common factors: 1, 2, 3, 4, 6, 12

12 divides both: 84 ÷ 12 = 7, 120 ÷ 12 = 10 — and 7 and 10 share no factor but 1, so no larger number divides both.

84 = 22 × 3 × 7

120 = 23 × 3 × 5

Prime84120Lowest power
2222322
3333
5—5—
77——

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

GCF = 22 × 3 = 12

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GCF Table

Number 1Number 2GCF
8410521
841062
841071
8410812
841091
841102
841113
8411228
841131
841146
841151
841164
841173
841182
841197
8412012
841211
841222
841233
841244
841251
8412642
841271
841284
841293
841302
841311
8413212
841337
841342

FAQ

What is the Greatest Common Divisor of 84 and 120?

GCF (HCF) of 84 and 120 is 12

How to find the GCF of 84 and 120?

You can find the GCF of 84 and 120 by listing all factors of both numbers and picking the greatest common one, or by prime factorization. The GCF of 84 and 120 is 12.

What prime factors do 84 and 120 share?

The prime factorizations of 84 and 120 have 2 × 2 × 3 in common, and multiplying those shared primes gives 12 — exactly the greatest common factor.

How does the GCF reduce the fraction 84/120?

Divide the numerator and the denominator by the GCF 12: 84 ÷ 12 = 7 and 120 ÷ 12 = 10. So 84/120 in lowest terms is 7/10.

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