GCF (HCF) of 75 and 1000

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What is the Greatest Common Divisor of 75 and 1,000?

Answer

GCF (HCF) of 75 and 1,000 is
25

Common factors: 1, 5, 25

25 divides both: 75 ÷ 25 = 3; 1,000 ÷ 25 = 40 — and 3 and 40 share no factor but 1, so no larger number divides both.

75 = 3 × 52

1,000 = 23 × 53

Prime751,000Lowest power
2—23—
33——
5525352

— = 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
759855
759861
759873
759881
759891
7599015
759911
759921
759933
759941
759955
759963
759971
759981
759993
751,00025
751,0011
751,0023
751,0031
751,0041
751,00515
751,0061
751,0071
751,0083
751,0091
751,0105
751,0113
751,0121
751,0131
751,0143

FAQ

What is the Greatest Common Divisor of 75 and 1,000?

GCF (HCF) of 75 and 1,000 is 25

How to find the GCF of 75 and 1,000?

You can find the GCF of 75 and 1,000 by listing all factors of both numbers and picking the greatest common one, or by prime factorization. The GCF of 75 and 1,000 is 25.

What prime factors do 75 and 1,000 share?

The prime factorizations of 75 and 1,000 have 5 × 5 in common, and multiplying those shared primes gives 25 — exactly the greatest common factor.

How does the GCF reduce the fraction 75/1000?

Divide the numerator and the denominator by the GCF 25: 75 ÷ 25 = 3 and 1,000 ÷ 25 = 40. So 75/1000 in lowest terms is 3/40.

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