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    GCF for 36, 48 and 144

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

    What's the Greatest Common Factor (GCF) of 36, 48 and 144?

    Answer

    GCF of 36, 48 and 144 is
    12

    (Twelve)

    12 is the largest positive integer that divides 36, 48 and 144 without a remainder — every other common divisor of the three divides it too.

    Finding the GCF of 36, 48 and 144 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 36: 2 × 2 × 3 × 3 (exponent form: 22 × 32)

    All Prime Factors of 48: 2 × 2 × 2 × 2 × 3 (exponent form: 24 × 3)

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

    Prime factor3648144Lowest power
    222242422
    3323323

    GCF = 2 × 2 × 3 = 12

    Checking the GCF of 36, 48 and 144 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(36, 48) = 12

    GCF(12, 144) = 12

    GCF(36, 48, 144) = 12

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

    36 ÷ 12 = 3

    48 ÷ 12 = 4

    144 ÷ 12 = 12

    3, 4 and 12 have no common factor left — that is what makes 12 the greatest one.

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    What is the GCF of 36, 48 and 144?. The GCF of 36, 48 and 144 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
    36481293
    36481302
    36481311
    364813212
    36481331
    36481342
    36481353
    36481364
    36481371
    36481386
    36481391
    36481404
    36481413
    36481422
    36481431
    364814412
    36481451
    36481462
    36481473
    36481484
    36481491
    36481506
    36481511
    36481524
    36481533
    36481542
    36481551
    364815612
    36481571
    36481582

    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 36, 48 and 144? (The answer is: 12). Enter the first number (e.g. '36'), the second (e.g. '48') and the third (e.g. '144'), 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 36, 48 and 144?

    GCF of 36, 48 and 144 is 12

    What prime factors do 36, 48 and 144 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 36, 48 and 144 two numbers at a time?

    Yes, and it is the check this page prints. The GCF of 36 and 48 is 12, and the GCF of 12 and 144 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 36 : 48 : 144?

    Divide every term by the GCF 12: 36 ÷ 12 = 3, 48 ÷ 12 = 4 and 144 ÷ 12 = 12. So 36 : 48 : 144 in lowest terms is 3 : 4 : 12, and no whole number other than 1 divides all three of those.

    See Also