GCF (HCF) of 45 and 120

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What is the Greatest Common Divisor of 45 and 120?

Answer

GCF (HCF) of 45 and 120 is
15

Common factors: 1, 3, 5, 15

15 divides both: 45 ÷ 15 = 3, 120 ÷ 15 = 8 — and 3 and 8 share no factor but 1, so no larger number divides both.

45 = 32 × 5

120 = 23 × 3 × 5

Prime45120Lowest power
2—23—
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
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
4518045
4540545

FAQ

What is the Greatest Common Divisor of 45 and 120?

GCF (HCF) of 45 and 120 is 15

How to find the GCF of 45 and 120?

You can find the GCF of 45 and 120 by listing all factors of both numbers and picking the greatest common one, or by prime factorization. The GCF of 45 and 120 is 15.

What prime factors do 45 and 120 share?

The prime factorizations of 45 and 120 have 3 × 5 in common, and multiplying those shared primes gives 15 — exactly the greatest common factor.

How does the GCF reduce the fraction 45/120?

Divide the numerator and the denominator by the GCF 15: 45 ÷ 15 = 3 and 120 ÷ 15 = 8. So 45/120 in lowest terms is 3/8.

See Also