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GCF for 2, 12 and 16

"Greatest Common Factor of 3 Numbers" Calculator

What's the Greatest Common Factor (GCF) of 2, 12 and 16?

Answer

GCF of 2, 12 and 16 is

(Two)

2 is the largest positive integer that divides 2, 12 and 16 without a remainder — every other common divisor of the three divides it too.

Finding the GCF of 2, 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 2: 2 (exponent form: 2)

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 factor	2	12	16	Lowest power
2	2	2²	2⁴	2
3	—	3	—	—

GCF = 2 = 2

Checking the GCF of 2, 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(2, 12) = 2

GCF(2, 16) = 2

GCF(2, 12, 16) = 2

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

2 ÷ 2 = 1

12 ÷ 2 = 6

16 ÷ 2 = 8

1, 6 and 8 have no common factor left — that is what makes 2 the greatest one.

Found an error in the calculation or the information?

Related Calculations

GCF Table

Number 1	Number 2	Number 3	GCF
1	2	12	1
2	2	12	2
2	3	12	1
2	4	12	2
2	5	12	1
2	6	12	2
2	7	12	1
2	8	12	2
2	9	12	1
2	10	12	2
2	11	12	1
2	12	12	2
2	12	13	1
2	12	14	2
2	12	15	1
2	12	16	2
2	12	17	1
2	12	18	2
2	12	19	1
2	12	20	2
2	12	21	1
2	12	22	2
2	12	23	1
2	12	24	2
2	12	25	1
2	12	26	2
2	12	27	1
2	12	28	2
2	12	29	1
2	12	30	2

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 2, 12 and 16? (The answer is: 2). Enter the first number (e.g. '2'), 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

FAQ

What's the Greatest Common Factor (GCF) of 2, 12 and 16?

GCF of 2, 12 and 16 is 2

What prime factors do 2, 12 and 16 share?

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

Can you get the GCF of 2, 12 and 16 two numbers at a time?

Yes, and it is the check this page prints. The GCF of 2 and 12 is 2, and the GCF of 2 and 16 is 2 — 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 2 : 12 : 16?

Divide every term by the GCF 2: 2 ÷ 2 = 1, 12 ÷ 2 = 6 and 16 ÷ 2 = 8. So 2 : 12 : 16 in lowest terms is 1 : 6 : 8, and no whole number other than 1 divides all three of those.

GCF for 2, 12 and 16

What's the Greatest Common Factor (GCF) of 2, 12 and 16?

Finding the GCF of 2, 12 and 16 by Prime Factorization

Checking the GCF of 2, 12 and 16 Two Numbers at a Time

Related Calculations

See Also

GCF Table

About "Greatest Common Factor of 3 Numbers" Calculator

FAQ

What's the Greatest Common Factor (GCF) of 2, 12 and 16?

What prime factors do 2, 12 and 16 share?

Can you get the GCF of 2, 12 and 16 two numbers at a time?

How does the GCF simplify the ratio 2 : 12 : 16?

See Also

Number 1	Number 2	Number 3	GCF
1	2	12	1
2	2	12	2
2	3	12	1
2	4	12	2
2	5	12	1
2	6	12	2
2	7	12	1
2	8	12	2
2	9	12	1
2	10	12	2
2	11	12	1
2	12	12	2
2	12	13	1
2	12	14	2
2	12	15	1
2	12	16	2
2	12	17	1
2	12	18	2
2	12	19	1
2	12	20	2
2	12	21	1
2	12	22	2
2	12	23	1
2	12	24	2
2	12	25	1
2	12	26	2
2	12	27	1
2	12	28	2
2	12	29	1
2	12	30	2

Number 1	Number 2	Number 3	GCF
1	2	12	1
2	2	12	2
2	3	12	1
2	4	12	2
2	5	12	1
2	6	12	2
2	7	12	1
2	8	12	2
2	9	12	1
2	10	12	2
2	11	12	1
2	12	12	2
2	12	13	1
2	12	14	2
2	12	15	1
2	12	16	2
2	12	17	1
2	12	18	2
2	12	19	1
2	12	20	2
2	12	21	1
2	12	22	2
2	12	23	1
2	12	24	2
2	12	25	1
2	12	26	2
2	12	27	1
2	12	28	2
2	12	29	1
2	12	30	2

Number 1	Number 2	Number 3	GCF
1	2	12	1
2	2	12	2
2	3	12	1
2	4	12	2
2	5	12	1
2	6	12	2
2	7	12	1
2	8	12	2
2	9	12	1
2	10	12	2
2	11	12	1
2	12	12	2
2	12	13	1
2	12	14	2
2	12	15	1
2	12	16	2
2	12	17	1
2	12	18	2
2	12	19	1
2	12	20	2
2	12	21	1
2	12	22	2
2	12	23	1
2	12	24	2
2	12	25	1
2	12	26	2
2	12	27	1
2	12	28	2
2	12	29	1
2	12	30	2