GCF (HCF) of 45 and 180

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What is the Greatest Common Divisor of 45 and 180?

Answer

GCF (HCF) of 45 and 180 is
45

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

45 divides 180 (180 ÷ 45 = 4), so the GCF is the smaller number itself.

45 = 32 × 5

180 = 22 × 32 × 5

Prime45180Lowest power
2—22—
3323232
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
45483
45491
45505
45513
45521
45549
45555
45561
456015
45639
45655
45705
45729
457515
45761
45805
45819
459045
45955
45999
451005
4510515
451089
451179
4512015
451255
4513545
4515015
4518045
4540545

FAQ

What is the Greatest Common Divisor of 45 and 180?

GCF (HCF) of 45 and 180 is 45

How to find the GCF of 45 and 180?

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

What prime factors do 45 and 180 share?

The prime factorizations of 45 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 45/180?

Divide the numerator and the denominator by the GCF 45: 45 ÷ 45 = 1 and 180 ÷ 45 = 4. So 45/180 in lowest terms is 1/4.

See Also