GCF (HCF) of 75 and 300

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What is the Greatest Common Divisor of 75 and 300?

Answer

GCF (HCF) of 75 and 300 is
75

Common factors: 1, 3, 5, 15, 25, 75

75 divides 300 (300 ÷ 75 = 4), so the GCF is the smaller number itself.

75 = 3 × 52

300 = 22 × 3 × 52

Prime75300Lowest power
2—22—
3333
5525252

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

GCF = 3 × 52 = 75

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GCF Table

Number 1Number 2GCF
7528515
752861
752871
752883
752891
752905
752913
752921
752931
752943
752955
752961
752973
752981
752991
7530075
753011
753021
753033
753041
753055
753063
753071
753081
753093
753105
753111
753123
753131
753141

FAQ

What is the Greatest Common Divisor of 75 and 300?

GCF (HCF) of 75 and 300 is 75

How to find the GCF of 75 and 300?

You can find the GCF of 75 and 300 by listing all factors of both numbers and picking the greatest common one, or by prime factorization. The GCF of 75 and 300 is 75.

What prime factors do 75 and 300 share?

The prime factorizations of 75 and 300 have 3 × 5 × 5 in common, and multiplying those shared primes gives 75 — exactly the greatest common factor.

How does the GCF reduce the fraction 75/300?

Divide the numerator and the denominator by the GCF 75: 75 ÷ 75 = 1 and 300 ÷ 75 = 4. So 75/300 in lowest terms is 1/4.

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