GCF (HCF) of 135 and 180

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What is the Greatest Common Divisor of 135 and 180?

Answer

GCF (HCF) of 135 and 180 is
45

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

45 divides both: 135 ÷ 45 = 3, 180 ÷ 45 = 4 — and 3 and 4 share no factor but 1, so no larger number divides both.

135 = 33 × 5

180 = 22 × 32 × 5

Prime135180Lowest power
2—22—
3333232
5555

— = 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
13516515
1351661
1351671
1351683
1351691
1351705
1351719
1351721
1351731
1351743
1351755
1351761
1351773
1351781
1351791
13518045
1351811
1351821
1351833
1351841
1351855
1351863
1351871
1351881
13518927
1351905
1351911
1351923
1351931
1351941

FAQ

What is the Greatest Common Divisor of 135 and 180?

GCF (HCF) of 135 and 180 is 45

How to find the GCF of 135 and 180?

You can find the GCF of 135 and 180 by listing all factors of both numbers and picking the greatest common one, or by prime factorization. The GCF of 135 and 180 is 45.

What prime factors do 135 and 180 share?

The prime factorizations of 135 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 135/180?

Divide the numerator and the denominator by the GCF 45: 135 ÷ 45 = 3 and 180 ÷ 45 = 4. So 135/180 in lowest terms is 3/4.

See Also