GCF (HCF) of 54 and 126

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What is the Greatest Common Divisor of 54 and 126?

Answer

GCF (HCF) of 54 and 126 is
18

Common factors: 1, 2, 3, 6, 9, 18

18 divides both: 54 ÷ 18 = 3, 126 ÷ 18 = 7 — and 3 and 7 share no factor but 1, so no larger number divides both.

54 = 2 × 33

126 = 2 × 32 × 7

Prime54126Lowest power
2222
3333232
7—7—

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

GCF = 2 × 32 = 18

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GCF Table

Number 1Number 2GCF
541113
541122
541131
541146
541151
541162
541179
541182
541191
541206
541211
541222
541233
541242
541251
5412618
541271
541282
541293
541302
541311
541326
541331
541342
5413527
541362
541371
541386
541391
541402

FAQ

What is the Greatest Common Divisor of 54 and 126?

GCF (HCF) of 54 and 126 is 18

How to find the GCF of 54 and 126?

You can find the GCF of 54 and 126 by listing all factors of both numbers and picking the greatest common one, or by prime factorization. The GCF of 54 and 126 is 18.

What prime factors do 54 and 126 share?

The prime factorizations of 54 and 126 have 2 × 3 × 3 in common, and multiplying those shared primes gives 18 — exactly the greatest common factor.

How does the GCF reduce the fraction 54/126?

Divide the numerator and the denominator by the GCF 18: 54 ÷ 18 = 3 and 126 ÷ 18 = 7. So 54/126 in lowest terms is 3/7.

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