GCF (HCF) of 175 and 400

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What is the Greatest Common Divisor of 175 and 400?

Answer

GCF (HCF) of 175 and 400 is
25

Common factors: 1, 5, 25

25 divides both: 175 ÷ 25 = 7, 400 ÷ 25 = 16 — and 7 and 16 share no factor but 1, so no larger number divides both.

175 = 52 × 7

400 = 24 × 52

Prime175400Lowest power
2—24—
5525252
77——

— = 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
17538535
1753861
1753871
1753881
1753891
1753905
1753911
1753927
1753931
1753941
1753955
1753961
1753971
1753981
1753997
17540025
1754011
1754021
1754031
1754041
1754055
1754067
1754071
1754081
1754091
1754105
1754111
1754121
1754137
1754141

FAQ

What is the Greatest Common Divisor of 175 and 400?

GCF (HCF) of 175 and 400 is 25

How to find the GCF of 175 and 400?

You can find the GCF of 175 and 400 by listing all factors of both numbers and picking the greatest common one, or by prime factorization. The GCF of 175 and 400 is 25.

What prime factors do 175 and 400 share?

The prime factorizations of 175 and 400 have 5 × 5 in common, and multiplying those shared primes gives 25 — exactly the greatest common factor.

How does the GCF reduce the fraction 175/400?

Divide the numerator and the denominator by the GCF 25: 175 ÷ 25 = 7 and 400 ÷ 25 = 16. So 175/400 in lowest terms is 7/16.

See Also