GCF (HCF) of 75 and 105

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What is the Greatest Common Divisor of 75 and 105?

Answer

GCF (HCF) of 75 and 105 is
15

Common factors: 1, 3, 5, 15

15 divides both: 75 ÷ 15 = 5, 105 ÷ 15 = 7 — and 5 and 7 share no factor but 1, so no larger number divides both.

75 = 3 × 52

105 = 3 × 5 × 7

Prime75105Lowest power
3333
55255
7—7—

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

GCF = 3 × 5 = 15

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GCF Table

Number 1Number 2GCF
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
751155
751161
751173
751181
751191

FAQ

What is the Greatest Common Divisor of 75 and 105?

GCF (HCF) of 75 and 105 is 15

How to find the GCF of 75 and 105?

You can find the GCF of 75 and 105 by listing all factors of both numbers and picking the greatest common one, or by prime factorization. The GCF of 75 and 105 is 15.

What prime factors do 75 and 105 share?

The prime factorizations of 75 and 105 have 3 × 5 in common, and multiplying those shared primes gives 15 — exactly the greatest common factor.

How does the GCF reduce the fraction 75/105?

Divide the numerator and the denominator by the GCF 15: 75 ÷ 15 = 5 and 105 ÷ 15 = 7. So 75/105 in lowest terms is 5/7.

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