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    Greatest Common Factor

    Find the Greatest Common Factor (GCF) of two numbers

    "Greatest Common Factor" Calculator

    Greatest Common Factor of
    and

    How to find the GCF of 12 and 16

    The greatest common factor (GCF) of two numbers is the largest natural number that divides both of them; it is also called the GCD or HCF.

    12 = 22 × 3

    16 = 24

    Prime1216Lowest power
    2222422
    33——

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

    GCF = 22 = 4

    Rule: factor each number into primes; the GCF multiplies every prime the numbers share, each at its lowest power.

    Frequent pairs
    NumbersGCF
    70 and 38535
    22 and 5511
    12 and 186
    32 and 17616
    135 and 18045
    24 and 3612
    20 and 3010
    45 and 6015
    16 and 451
    35 and 391

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    FAQ

    What is the greatest common factor of two numbers?

    It is the largest positive integer that divides both numbers with no remainder. The same value is also called the greatest common divisor (GCD) and the highest common factor (HCF) — three names for one number. For 12 and 16 it is 4.

    How do you find the GCF by prime factorization?

    Split both numbers into prime factors and multiply the primes they share, each taken as many times as it appears in both factorizations. 12 = 2 × 2 × 3 and 16 = 2 × 2 × 2 × 2 share 2 × 2, so the GCF is 4.

    What is the Euclidean algorithm for the GCF?

    Euclid described it in the Elements around 300 BC: divide the larger number by the smaller one, then replace the pair with the smaller number and the remainder, until the remainder is 0. For 16 and 12 that is 16 mod 12 = 4 and then 12 mod 4 = 0, so the GCF is 4. It never factorizes anything, which is why it stays fast on numbers far too large to factor.