GCF (HCF) of 315 and 180

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What is the Greatest Common Divisor of 315 and 180?

Answer

GCF (HCF) of 315 and 180 is
45

Common factors: 1, 3, 5, 9, 15, 45

45 divides both: 315 ÷ 45 = 7, 180 ÷ 45 = 4 — and 7 and 4 share no factor but 1, so no larger number divides both.

315 = 32 × 5 × 7

180 = 22 × 32 × 5

Prime315180Lowest power
2—22—
3323232
5555
77——

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

GCF = 32 × 5 = 45

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GCF Table

Number 1Number 2GCF
31516515
3151661
3151671
31516821
3151691
3151705
3151719
3151721
3151731
3151743
31517535
3151761
3151773
3151781
3151791
31518045
3151811
3151827
3151833
3151841
3151855
3151863
3151871
3151881
31518963
3151905
3151911
3151923
3151931
3151941

FAQ

What is the Greatest Common Divisor of 315 and 180?

GCF (HCF) of 315 and 180 is 45

How to find the GCF of 315 and 180?

You can find the GCF of 315 and 180 by listing all factors of both numbers and picking the greatest common one, or by prime factorization. The GCF of 315 and 180 is 45.

What prime factors do 315 and 180 share?

The prime factorizations of 315 and 180 have 3 × 3 × 5 in common, and multiplying those shared primes gives 45 — exactly the greatest common factor.

How does the GCF reduce the fraction 315/180?

Divide the numerator and the denominator by the GCF 45: 315 ÷ 45 = 7 and 180 ÷ 45 = 4. So 315/180 in lowest terms is 7/4.

See Also