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    GCF (HCF) of 120 and 168

    "Greatest Common Factor" Calculator
    Greatest Common Factor of
    and

    What is the Greatest Common Divisor of 120 and 168?

    Answer

    GCF (HCF) of 120 and 168 is
    24

    Common factors: 1, 2, 3, 4, 6, 8, 12, 24

    24 divides both: 120 ÷ 24 = 5, 168 ÷ 24 = 7 — and 5 and 7 share no factor but 1, so no larger number divides both.

    120 = 23 × 3 × 5

    168 = 23 × 3 × 7

    Prime120168Lowest power
    2232323
    3333
    55——
    7—7—

    — = power 0: the prime is not a factor of this number, so it cannot be in the GCF.

    GCF = 23 × 3 = 24

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    What is the GCF (HCF) of 120 and 168. The GCF of 120 and 168 is 24 — 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
    1201533
    1201542
    1201555
    12015612
    1201571
    1201582
    1201593
    12016040
    1201611
    1201626
    1201631
    1201644
    12016515
    1201662
    1201671
    12016824
    1201691
    12017010
    1201713
    1201724
    1201731
    1201746
    1201755
    1201768
    1201773
    1201782
    1201791
    12018060
    1201811
    1201822

    FAQ

    What is the Greatest Common Divisor of 120 and 168?

    GCF (HCF) of 120 and 168 is 24

    How to find the GCF of 120 and 168?

    You can find the GCF of 120 and 168 by listing all factors of both numbers and picking the greatest common one, or by prime factorization. The GCF of 120 and 168 is 24.

    What prime factors do 120 and 168 share?

    The prime factorizations of 120 and 168 have 2 × 2 × 2 × 3 in common, and multiplying those shared primes gives 24 — exactly the greatest common factor.

    How does the GCF reduce the fraction 120/168?

    Divide the numerator and the denominator by the GCF 24: 120 ÷ 24 = 5 and 168 ÷ 24 = 7. So 120/168 in lowest terms is 5/7.

    See Also