GCF (HCF) of 84 and 132

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What is the Greatest Common Divisor of 84 and 132?

Answer

GCF (HCF) of 84 and 132 is
12

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

12 divides both: 84 ÷ 12 = 7, 132 ÷ 12 = 11 — and 7 and 11 share no factor but 1, so no larger number divides both.

84 = 22 × 3 × 7

132 = 22 × 3 × 11

Prime84132Lowest power
2222222
3333
77——
11—11—

— = 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
841173
841182
841197
8412012
841211
841222
841233
841244
841251
8412642
841271
841284
841293
841302
841311
8413212
841337
841342
841353
841364
841371
841386
841391
8414028
841413
841422
841431
8414412
841451
841462

FAQ

What is the Greatest Common Divisor of 84 and 132?

GCF (HCF) of 84 and 132 is 12

How to find the GCF of 84 and 132?

You can find the GCF of 84 and 132 by listing all factors of both numbers and picking the greatest common one, or by prime factorization. The GCF of 84 and 132 is 12.

What prime factors do 84 and 132 share?

The prime factorizations of 84 and 132 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 84/132?

Divide the numerator and the denominator by the GCF 12: 84 ÷ 12 = 7 and 132 ÷ 12 = 11. So 84/132 in lowest terms is 7/11.

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