GCF for 48, 64 and 96

"Greatest Common Factor of 3 Numbers" Calculator
Greatest Common Factor of
,
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What's the Greatest Common Factor (GCF) of 48, 64 and 96?

Answer

GCF of 48, 64 and 96 is
16

(Sixteen)

16 is the largest positive integer that divides 48, 64 and 96 without a remainder — every other common divisor of the three divides it too.

Finding the GCF of 48, 64 and 96 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 48: 2 × 2 × 2 × 2 × 3 (exponent form: 24 × 3)

All Prime Factors of 64: 2 × 2 × 2 × 2 × 2 × 2 (exponent form: 26)

All Prime Factors of 96: 2 × 2 × 2 × 2 × 2 × 3 (exponent form: 25 × 3)

Prime factor486496Lowest power
224262524
33—3—

GCF = 2 × 2 × 2 × 2 = 16

Checking the GCF of 48, 64 and 96 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(48, 64) = 16

GCF(16, 96) = 16

GCF(48, 64, 96) = 16

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

48 ÷ 16 = 3

64 ÷ 16 = 4

96 ÷ 16 = 6

3, 4 and 6 have no common factor left — that is what makes 16 the greatest one.

Related Calculations

See Also

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 48, 64 and 96? (The answer is: 16). Enter the first number (e.g. '48'), the second (e.g. '64') and the third (e.g. '96'), 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

GCF Table

Number 1Number 2Number 3GCF
4864811
4864822
4864831
4864844
4864851
4864862
4864871
4864888
4864891
4864902
4864911
4864924
4864931
4864942
4864951
48649616
4864971
4864982
4864991
48641004
48641011
48641022
48641031
48641048
48641051
48641062
48641071
48641084
48641091
48641102

FAQ

What's the Greatest Common Factor (GCF) of 48, 64 and 96?

GCF of 48, 64 and 96 is 16

What prime factors do 48, 64 and 96 share?

All three factorizations contain 2 × 2 × 2 × 2, and multiplying those shared primes gives 16 — exactly the greatest common factor.

Can you get the GCF of 48, 64 and 96 two numbers at a time?

Yes, and it is the check this page prints. The GCF of 48 and 64 is 16, and the GCF of 16 and 96 is 16 — 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 48 : 64 : 96?

Divide every term by the GCF 16: 48 ÷ 16 = 3, 64 ÷ 16 = 4 and 96 ÷ 16 = 6. So 48 : 64 : 96 in lowest terms is 3 : 4 : 6, and no whole number other than 1 divides all three of those.

See Also