GCF for 8, 12 and 16

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

What's the Greatest Common Factor (GCF) of 8, 12 and 16?

Answer

GCF of 8, 12 and 16 is
4

(Four)

4 is the largest positive integer that divides 8, 12 and 16 without a remainder — every other common divisor of the three divides it too.

Finding the GCF of 8, 12 and 16 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 8: 2 × 2 × 2 (exponent form: 23)

All Prime Factors of 12: 2 × 2 × 3 (exponent form: 22 × 3)

All Prime Factors of 16: 2 × 2 × 2 × 2 (exponent form: 24)

Prime factor81216Lowest power
223222422
3—3——

GCF = 2 × 2 = 4

Checking the GCF of 8, 12 and 16 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(8, 12) = 4

GCF(4, 16) = 4

GCF(8, 12, 16) = 4

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

8 ÷ 4 = 2

12 ÷ 4 = 3

16 ÷ 4 = 4

2, 3 and 4 have no common factor left — that is what makes 4 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 8, 12 and 16? (The answer is: 4). Enter the first number (e.g. '8'), the second (e.g. '12') and the third (e.g. '16'), 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
18121
28122
38121
48124
58121
68122
78121
88124
89121
810122
811121
812124
812131
812142
812151
812164
812171
812182
812191
812204
812211
812222
812231
812244
812251
812262
812271
812284
812291
812302

FAQ

What's the Greatest Common Factor (GCF) of 8, 12 and 16?

GCF of 8, 12 and 16 is 4

What prime factors do 8, 12 and 16 share?

All three factorizations contain 2 × 2, and multiplying those shared primes gives 4 — exactly the greatest common factor.

Can you get the GCF of 8, 12 and 16 two numbers at a time?

Yes, and it is the check this page prints. The GCF of 8 and 12 is 4, and the GCF of 4 and 16 is 4 — 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 8 : 12 : 16?

Divide every term by the GCF 4: 8 ÷ 4 = 2, 12 ÷ 4 = 3 and 16 ÷ 4 = 4. So 8 : 12 : 16 in lowest terms is 2 : 3 : 4, and no whole number other than 1 divides all three of those.

See Also