GCF for 30, 60 and 90

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

What's the Greatest Common Factor (GCF) of 30, 60 and 90?

Answer

GCF of 30, 60 and 90 is
30

(Thirty)

30 is the largest positive integer that divides 30, 60 and 90 without a remainder — every other common divisor of the three divides it too.

Finding the GCF of 30, 60 and 90 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 30: 2 × 3 × 5 (exponent form: 2 × 3 × 5)

All Prime Factors of 60: 2 × 2 × 3 × 5 (exponent form: 22 × 3 × 5)

All Prime Factors of 90: 2 × 3 × 3 × 5 (exponent form: 2 × 32 × 5)

Prime factor306090Lowest power
222222
333323
55555

GCF = 2 × 3 × 5 = 30

Checking the GCF of 30, 60 and 90 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(30, 60) = 30

GCF(30, 90) = 30

GCF(30, 60, 90) = 30

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

30 ÷ 30 = 1

60 ÷ 30 = 2

90 ÷ 30 = 3

1, 2 and 3 have no common factor left — that is what makes 30 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 30, 60 and 90? (The answer is: 30). Enter the first number (e.g. '30'), the second (e.g. '60') and the third (e.g. '90'), 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
30607515
3060762
3060771
3060786
3060791
30608010
3060813
3060822
3060831
3060846
3060855
3060862
3060873
3060882
3060891
30609030
3060911
3060922
3060933
3060942
3060955
3060966
3060971
3060982
3060993
306010010
30601011
30601026
30601031
30601042

FAQ

What's the Greatest Common Factor (GCF) of 30, 60 and 90?

GCF of 30, 60 and 90 is 30

What prime factors do 30, 60 and 90 share?

All three factorizations contain 2 × 3 × 5, and multiplying those shared primes gives 30 — exactly the greatest common factor.

Can you get the GCF of 30, 60 and 90 two numbers at a time?

Yes, and it is the check this page prints. The GCF of 30 and 60 is 30, and the GCF of 30 and 90 is 30 — 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 30 : 60 : 90?

Divide every term by the GCF 30: 30 ÷ 30 = 1, 60 ÷ 30 = 2 and 90 ÷ 30 = 3. So 30 : 60 : 90 in lowest terms is 1 : 2 : 3, and no whole number other than 1 divides all three of those.

See Also