GCF (HCF) of 75 and 100

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What is the Greatest Common Divisor of 75 and 100?

Answer

GCF (HCF) of 75 and 100 is
25

Common factors: 1, 5, 25

25 divides both: 75 ÷ 25 = 3, 100 ÷ 25 = 4 — and 3 and 4 share no factor but 1, so no larger number divides both.

75 = 3 × 52

100 = 22 × 52

Prime75100Lowest power
2—22—
33——
5525252

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

GCF = 52 = 25

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GCF Table

Number 1Number 2GCF
75855
75861
75873
75881
75891
759015
75911
75921
75933
75941
75955
75963
75971
75981
75993
7510025
751011
751023
751031
751041
7510515
751061
751071
751083
751091
751105
751113
751121
751131
751143

FAQ

What is the Greatest Common Divisor of 75 and 100?

GCF (HCF) of 75 and 100 is 25

How to find the GCF of 75 and 100?

You can find the GCF of 75 and 100 by listing all factors of both numbers and picking the greatest common one, or by prime factorization. The GCF of 75 and 100 is 25.

What prime factors do 75 and 100 share?

The prime factorizations of 75 and 100 have 5 × 5 in common, and multiplying those shared primes gives 25 — exactly the greatest common factor.

How does the GCF reduce the fraction 75/100?

Divide the numerator and the denominator by the GCF 25: 75 ÷ 25 = 3 and 100 ÷ 25 = 4. So 75/100 in lowest terms is 3/4.

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