GCF (HCF) of 54 and 60

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What is the Greatest Common Divisor of 54 and 60?

Answer

GCF (HCF) of 54 and 60 is
6

Common factors: 1, 2, 3, 6

6 divides both: 54 ÷ 6 = 9, 60 ÷ 6 = 10 — and 9 and 10 share no factor but 1, so no larger number divides both.

54 = 2 × 33

60 = 22 × 3 × 5

Prime5460Lowest power
22222
33333
5—5—

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

GCF = 2 × 3 = 6

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GCF Table

Number 1Number 2GCF
54459
54462
54471
54486
54491
54502
54513
54522
54531
545454
54551
54562
54573
54582
54591
54606
54611
54622
54639
54642
54651
54666
54671
54682
54693
54702
54711
547218
54731
54742

FAQ

What is the Greatest Common Divisor of 54 and 60?

GCF (HCF) of 54 and 60 is 6

How to find the GCF of 54 and 60?

You can find the GCF of 54 and 60 by listing all factors of both numbers and picking the greatest common one, or by prime factorization. The GCF of 54 and 60 is 6.

What prime factors do 54 and 60 share?

The prime factorizations of 54 and 60 have 2 × 3 in common, and multiplying those shared primes gives 6 — exactly the greatest common factor.

How does the GCF reduce the fraction 54/60?

Divide the numerator and the denominator by the GCF 6: 54 ÷ 6 = 9 and 60 ÷ 6 = 10. So 54/60 in lowest terms is 9/10.

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