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    GCF (HCF) of 75 and 120

    "Greatest Common Factor" Calculator
    Greatest Common Factor of
    and

    What is the Greatest Common Divisor of 75 and 120?

    Answer

    GCF (HCF) of 75 and 120 is
    15

    Common factors: 1, 3, 5, 15

    15 divides both: 75 ÷ 15 = 5, 120 ÷ 15 = 8 — and 5 and 8 share no factor but 1, so no larger number divides both.

    75 = 3 × 52

    120 = 23 × 3 × 5

    Prime75120Lowest power
    2—23—
    3333
    55255

    — = 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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    What is the GCF (HCF) of 75 and 120. The GCF of 75 and 120 is 15 — 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
    7510515
    751061
    751071
    751083
    751091
    751105
    751113
    751121
    751131
    751143
    751155
    751161
    751173
    751181
    751191
    7512015
    751211
    751221
    751233
    751241
    7512525
    751263
    751271
    751281
    751293
    751305
    751311
    751323
    751331
    751341

    FAQ

    What is the Greatest Common Divisor of 75 and 120?

    GCF (HCF) of 75 and 120 is 15

    How to find the GCF of 75 and 120?

    You can find the GCF of 75 and 120 by listing all factors of both numbers and picking the greatest common one, or by prime factorization. The GCF of 75 and 120 is 15.

    What prime factors do 75 and 120 share?

    The prime factorizations of 75 and 120 have 3 × 5 in common, and multiplying those shared primes gives 15 — exactly the greatest common factor.

    How does the GCF reduce the fraction 75/120?

    Divide the numerator and the denominator by the GCF 15: 75 ÷ 15 = 5 and 120 ÷ 15 = 8. So 75/120 in lowest terms is 5/8.

    See Also