GCF (HCF) of 45 and 60

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What is the Greatest Common Divisor of 45 and 60?

Answer

GCF (HCF) of 45 and 60 is
15

Common factors: 1, 3, 5, 15

15 divides both: 45 ÷ 15 = 3, 60 ÷ 15 = 4 — and 3 and 4 share no factor but 1, so no larger number divides both.

45 = 32 × 5

60 = 22 × 3 × 5

Prime4560Lowest power
2—22—
33233
5555

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

GCF = 3 × 5 = 15

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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 60?

GCF (HCF) of 45 and 60 is 15

How to find the GCF of 45 and 60?

You can find the GCF of 45 and 60 by listing all factors of both numbers and picking the greatest common one, or by prime factorization. The GCF of 45 and 60 is 15.

What prime factors do 45 and 60 share?

The prime factorizations of 45 and 60 have 3 × 5 in common, and multiplying those shared primes gives 15 — exactly the greatest common factor.

How does the GCF reduce the fraction 45/60?

Divide the numerator and the denominator by the GCF 15: 45 ÷ 15 = 3 and 60 ÷ 15 = 4. So 45/60 in lowest terms is 3/4.

See Also