GCF (HCF) of 84 and 420

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What is the Greatest Common Divisor of 84 and 420?

Answer

GCF (HCF) of 84 and 420 is
84

Common factors: 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 84

84 divides 420 (420 ÷ 84 = 5), so the GCF is the smaller number itself.

84 = 22 × 3 × 7

420 = 22 × 3 × 5 × 7

Prime84420Lowest power
2222222
3333
5—5—
7777

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

GCF = 22 × 3 × 7 = 84

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GCF Table

Number 1Number 2GCF
844053
8440614
844071
8440812
844091
844102
844113
844124
844137
844146
844151
844164
844173
844182
844191
8442084
844211
844222
844233
844244
844251
844266
844277
844284
844293
844302
844311
8443212
844331
8443414

FAQ

What is the Greatest Common Divisor of 84 and 420?

GCF (HCF) of 84 and 420 is 84

How to find the GCF of 84 and 420?

You can find the GCF of 84 and 420 by listing all factors of both numbers and picking the greatest common one, or by prime factorization. The GCF of 84 and 420 is 84.

What prime factors do 84 and 420 share?

The prime factorizations of 84 and 420 have 2 × 2 × 3 × 7 in common, and multiplying those shared primes gives 84 — exactly the greatest common factor.

How does the GCF reduce the fraction 84/420?

Divide the numerator and the denominator by the GCF 84: 84 ÷ 84 = 1 and 420 ÷ 84 = 5. So 84/420 in lowest terms is 1/5.

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