GCF (HCF) of 225 and 180

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What is the Greatest Common Divisor of 225 and 180?

Answer

GCF (HCF) of 225 and 180 is
45

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

45 divides both: 225 ÷ 45 = 5, 180 ÷ 45 = 4 — and 5 and 4 share no factor but 1, so no larger number divides both.

225 = 32 × 52

180 = 22 × 32 × 5

Prime225180Lowest power
2—22—
3323232
55255

— = 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
22516515
2251661
2251671
2251683
2251691
2251705
2251719
2251721
2251731
2251743
22517525
2251761
2251773
2251781
2251791
22518045
2251811
2251821
2251833
2251841
2251855
2251863
2251871
2251881
2251899
2251905
2251911
2251923
2251931
2251941

FAQ

What is the Greatest Common Divisor of 225 and 180?

GCF (HCF) of 225 and 180 is 45

How to find the GCF of 225 and 180?

You can find the GCF of 225 and 180 by listing all factors of both numbers and picking the greatest common one, or by prime factorization. The GCF of 225 and 180 is 45.

What prime factors do 225 and 180 share?

The prime factorizations of 225 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 225/180?

Divide the numerator and the denominator by the GCF 45: 225 ÷ 45 = 5 and 180 ÷ 45 = 4. So 225/180 in lowest terms is 5/4.

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