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    GCF (HCF) of 75 and 100

    "Greatest Common Factor" Calculator
    Greatest Common Factor of
    and

    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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    What is the GCF (HCF) of 75 and 100. The GCF of 75 and 100 is 25 — the biggest number that can divide both integers. Step-by-step GCF (GCD) calculation by factoring.
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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.

    See Also