GCF (HCF) of 75 and 180

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What is the Greatest Common Divisor of 75 and 180?

Answer

GCF (HCF) of 75 and 180 is
15

Common factors: 1, 3, 5, 15

15 divides both: 75 ÷ 15 = 5, 180 ÷ 15 = 12 — and 5 and 12 share no factor but 1, so no larger number divides both.

75 = 3 × 52

180 = 22 × 32 × 5

Prime75180Lowest power
2—22—
33323
55255

— = 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
7516515
751661
751671
751683
751691
751705
751713
751721
751731
751743
7517525
751761
751773
751781
751791
7518015
751811
751821
751833
751841
751855
751863
751871
751881
751893
751905
751911
751923
751931
751941

FAQ

What is the Greatest Common Divisor of 75 and 180?

GCF (HCF) of 75 and 180 is 15

How to find the GCF of 75 and 180?

You can find the GCF of 75 and 180 by listing all factors of both numbers and picking the greatest common one, or by prime factorization. The GCF of 75 and 180 is 15.

What prime factors do 75 and 180 share?

The prime factorizations of 75 and 180 have 3 × 5 in common, and multiplying those shared primes gives 15 — exactly the greatest common factor.

How does the GCF reduce the fraction 75/180?

Divide the numerator and the denominator by the GCF 15: 75 ÷ 15 = 5 and 180 ÷ 15 = 12. So 75/180 in lowest terms is 5/12.

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