GCF (HCF) of 210 and 180

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What is the Greatest Common Divisor of 210 and 180?

Answer

GCF (HCF) of 210 and 180 is
30

Common factors: 1, 2, 3, 5, 6, 10, 15, 30

30 divides both: 210 ÷ 30 = 7, 180 ÷ 30 = 6 — and 7 and 6 share no factor but 1, so no larger number divides both.

210 = 2 × 3 × 5 × 7

180 = 22 × 32 × 5

Prime210180Lowest power
22222
33323
5555
77——

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

GCF = 2 × 3 × 5 = 30

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GCF Table

Number 1Number 2GCF
21016515
2101662
2101671
21016842
2101691
21017010
2101713
2101722
2101731
2101746
21017535
2101762
2101773
2101782
2101791
21018030
2101811
21018214
2101833
2101842
2101855
2101866
2101871
2101882
21018921
21019010
2101911
2101926
2101931
2101942

FAQ

What is the Greatest Common Divisor of 210 and 180?

GCF (HCF) of 210 and 180 is 30

How to find the GCF of 210 and 180?

You can find the GCF of 210 and 180 by listing all factors of both numbers and picking the greatest common one, or by prime factorization. The GCF of 210 and 180 is 30.

What prime factors do 210 and 180 share?

The prime factorizations of 210 and 180 have 2 × 3 × 5 in common, and multiplying those shared primes gives 30 — exactly the greatest common factor.

How does the GCF reduce the fraction 210/180?

Divide the numerator and the denominator by the GCF 30: 210 ÷ 30 = 7 and 180 ÷ 30 = 6. So 210/180 in lowest terms is 7/6.

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