GCF (HCF) of 75 and 350

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What is the Greatest Common Divisor of 75 and 350?

Answer

GCF (HCF) of 75 and 350 is
25

Common factors: 1, 5, 25

25 divides both: 75 ÷ 25 = 3, 350 ÷ 25 = 14 — and 3 and 14 share no factor but 1, so no larger number divides both.

75 = 3 × 52

350 = 2 × 52 × 7

Prime75350Lowest power
2—2—
33——
5525252
7—7—

— = 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
753355
753363
753371
753381
753393
753405
753411
753423
753431
753441
7534515
753461
753471
753483
753491
7535025
753513
753521
753531
753543
753555
753561
753573
753581
753591
7536015
753611
753621
753633
753641

FAQ

What is the Greatest Common Divisor of 75 and 350?

GCF (HCF) of 75 and 350 is 25

How to find the GCF of 75 and 350?

You can find the GCF of 75 and 350 by listing all factors of both numbers and picking the greatest common one, or by prime factorization. The GCF of 75 and 350 is 25.

What prime factors do 75 and 350 share?

The prime factorizations of 75 and 350 have 5 × 5 in common, and multiplying those shared primes gives 25 — exactly the greatest common factor.

How does the GCF reduce the fraction 75/350?

Divide the numerator and the denominator by the GCF 25: 75 ÷ 25 = 3 and 350 ÷ 25 = 14. So 75/350 in lowest terms is 3/14.

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