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    GCF for 120, 144 and 324

    "Greatest Common Factor of 3 Numbers" Calculator
    Greatest Common Factor of
    ,
    and

    What's the Greatest Common Factor (GCF) of 120, 144 and 324?

    Answer

    GCF of 120, 144 and 324 is
    12

    (Twelve)

    12 is the largest positive integer that divides 120, 144 and 324 without a remainder — every other common divisor of the three divides it too.

    Finding the GCF of 120, 144 and 324 by Prime Factorization

    Split all three numbers into prime factors, then keep every prime that appears in all three of them, each taken as many times as it appears in the poorest factorization. Multiplying what is left gives the greatest common factor:

    All Prime Factors of 120: 2 × 2 × 2 × 3 × 5 (exponent form: 23 × 3 × 5)

    All Prime Factors of 144: 2 × 2 × 2 × 2 × 3 × 3 (exponent form: 24 × 32)

    All Prime Factors of 324: 2 × 2 × 3 × 3 × 3 × 3 (exponent form: 22 × 34)

    Prime factor120144324Lowest power
    223242222
    3332343
    55———

    GCF = 2 × 2 × 3 = 12

    Checking the GCF of 120, 144 and 324 Two Numbers at a Time

    The greatest common factor is associative, so three numbers can be handled as two pairs — and this is what makes the Euclidean algorithm usable here: run it on the first pair, then run it again on that result and the third number.

    GCF(a, b, c) = GCF(GCF(a, b), c)

    GCF(120, 144) = 24

    GCF(24, 324) = 12

    GCF(120, 144, 324) = 12

    The answer checks out by division — all three quotients come out whole:

    120 ÷ 12 = 10

    144 ÷ 12 = 12

    324 ÷ 12 = 27

    10, 12 and 27 have no common factor left — that is what makes 12 the greatest one.

    Related Calculations

    See Also

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    What is the GCF of 120, 144 and 324?. The GCF of 120, 144 and 324 is 12 — the largest number that divides all three with no remainder. Step-by-step solution for three numbers.
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    GCF Table

    Number 1Number 2Number 3GCF
    1201443093
    1201443102
    1201443111
    12014431224
    1201443131
    1201443142
    1201443153
    1201443164
    1201443171
    1201443186
    1201443191
    1201443208
    1201443213
    1201443222
    1201443231
    12014432412
    1201443251
    1201443262
    1201443273
    1201443288
    1201443291
    1201443306
    1201443311
    1201443324
    1201443333
    1201443342
    1201443351
    12014433624
    1201443371
    1201443382

    About "Greatest Common Factor of 3 Numbers" Calculator

    This calculator finds the Greatest Common Factor (GCF) of three numbers at once, without doing it in two passes. For example, it can help you find out what's the Greatest Common Factor (GCF) of 120, 144 and 324? (The answer is: 12). Enter the first number (e.g. '120'), the second (e.g. '144') and the third (e.g. '324'), then hit the 'Calculate' button.
    The Greatest Common Factor of three numbers — also called the greatest common divisor (GCD) or highest common factor (HCF) — is the largest positive integer that divides all three of them with zero remainder
    "Greatest Common Factor of 3 Numbers" Calculator
    Greatest Common Factor of
    ,
    and

    FAQ

    What's the Greatest Common Factor (GCF) of 120, 144 and 324?

    GCF of 120, 144 and 324 is 12

    What prime factors do 120, 144 and 324 share?

    All three factorizations contain 2 × 2 × 3, and multiplying those shared primes gives 12 — exactly the greatest common factor.

    Can you get the GCF of 120, 144 and 324 two numbers at a time?

    Yes, and it is the check this page prints. The GCF of 120 and 144 is 24, and the GCF of 24 and 324 is 12 — the same answer, because the greatest common factor is associative and does not depend on the order of the three numbers.

    How does the GCF simplify the ratio 120 : 144 : 324?

    Divide every term by the GCF 12: 120 ÷ 12 = 10, 144 ÷ 12 = 12 and 324 ÷ 12 = 27. So 120 : 144 : 324 in lowest terms is 10 : 12 : 27, and no whole number other than 1 divides all three of those.

    See Also