GCF (HCF) of 84 and 126

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What is the Greatest Common Divisor of 84 and 126?

Answer

GCF (HCF) of 84 and 126 is
42

Common factors: 1, 2, 3, 6, 7, 14, 21, 42

42 divides both: 84 ÷ 42 = 2, 126 ÷ 42 = 3 — and 2 and 3 share no factor but 1, so no larger number divides both.

84 = 22 × 3 × 7

126 = 2 × 32 × 7

Prime84126Lowest power
22222
33323
7777

GCF = 2 × 3 × 7 = 42

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GCF Table

Number 1Number 2GCF
841113
8411228
841131
841146
841151
841164
841173
841182
841197
8412012
841211
841222
841233
841244
841251
8412642
841271
841284
841293
841302
841311
8413212
841337
841342
841353
841364
841371
841386
841391
8414028

FAQ

What is the Greatest Common Divisor of 84 and 126?

GCF (HCF) of 84 and 126 is 42

How to find the GCF of 84 and 126?

You can find the GCF of 84 and 126 by listing all factors of both numbers and picking the greatest common one, or by prime factorization. The GCF of 84 and 126 is 42.

What prime factors do 84 and 126 share?

The prime factorizations of 84 and 126 have 2 × 3 × 7 in common, and multiplying those shared primes gives 42 — exactly the greatest common factor.

How does the GCF reduce the fraction 84/126?

Divide the numerator and the denominator by the GCF 42: 84 ÷ 42 = 2 and 126 ÷ 42 = 3. So 84/126 in lowest terms is 2/3.

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