GCF for 3, 5 and 7

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

What's the Greatest Common Factor (GCF) of 3, 5 and 7?

Answer

GCF of 3, 5 and 7 is
1

(One)

1 is the largest positive integer that divides 3, 5 and 7 without a remainder — every other common divisor of the three divides it too.

Finding the GCF of 3, 5 and 7 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 3: 3 (exponent form: 3)

All Prime Factors of 5: 5 (exponent form: 5)

All Prime Factors of 7: 7 (exponent form: 7)

Prime factor357Lowest power
33———
5—5——
7——7—

Not one prime factor is shared by all three numbers, which makes 3, 5 and 7 relatively prime as a set. The only positive integer dividing all of them is 1.

Checking the GCF of 3, 5 and 7 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(3, 5) = 1

GCF(1, 7) = 1

GCF(3, 5, 7) = 1

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

3 ÷ 1 = 3

5 ÷ 1 = 5

7 ÷ 1 = 7

3, 5 and 7 have no common factor left — that is what makes 1 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 3, 5 and 7? (The answer is: 1). Enter the first number (e.g. '3'), the second (e.g. '5') and the third (e.g. '7'), 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
1351
2351
3351
3451
3551
3561
3571
3581
3591
35101
35111
35121
35131
35141
35151
35161
35171
35181
35191
35201
35211
35221
35231
35241
35251
35261
35271
35281
35291
35301

FAQ

What's the Greatest Common Factor (GCF) of 3, 5 and 7?

GCF of 3, 5 and 7 is 1

What prime factors do 3, 5 and 7 share?

None at all: 3, 5 and 7 have no prime factor in common, so the only positive integer dividing all three is 1 and their GCF is 1.

Can you get the GCF of 3, 5 and 7 two numbers at a time?

Yes, and it is the check this page prints. The GCF of 3 and 5 is 1, and the GCF of 1 and 7 is 1 — 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 3 : 5 : 7?

Divide every term by the GCF 1: 3 ÷ 1 = 3, 5 ÷ 1 = 5 and 7 ÷ 1 = 7. So 3 : 5 : 7 in lowest terms is 3 : 5 : 7, and no whole number other than 1 divides all three of those.

See Also