GCF (HCF) of 45 and 54

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What is the Greatest Common Divisor of 45 and 54?

Answer

GCF (HCF) of 45 and 54 is
9

Common factors: 1, 3, 9

9 divides both: 45 ÷ 9 = 5, 54 ÷ 9 = 6 — and 5 and 6 share no factor but 1, so no larger number divides both.

45 = 32 × 5

54 = 2 × 33

Prime4554Lowest power
2—2—
3323332
55——

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

GCF = 32 = 9

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GCF Table

Number 1Number 2GCF
451515
453015
45483
45491
45505
45513
45521
45549
45555
45561
456015
45639
45655
45705
45729
457515
45761
45805
45819
459045
45955
45999
451005
4510515
451089
451179
4512015
451255
4513545
4515015

FAQ

What is the Greatest Common Divisor of 45 and 54?

GCF (HCF) of 45 and 54 is 9

How to find the GCF of 45 and 54?

You can find the GCF of 45 and 54 by listing all factors of both numbers and picking the greatest common one, or by prime factorization. The GCF of 45 and 54 is 9.

What prime factors do 45 and 54 share?

The prime factorizations of 45 and 54 have 3 × 3 in common, and multiplying those shared primes gives 9 — exactly the greatest common factor.

How does the GCF reduce the fraction 45/54?

Divide the numerator and the denominator by the GCF 9: 45 ÷ 9 = 5 and 54 ÷ 9 = 6. So 45/54 in lowest terms is 5/6.

See Also