GCF for 60, 90 and 120

"Greatest Common Factor of 3 Numbers" Calculator

What's the Greatest Common Factor (GCF) of 60, 90 and 120?

Answer

GCF of 60, 90 and 120 is

(Thirty)

30 is the largest positive integer that divides 60, 90 and 120 without a remainder — every other common divisor of the three divides it too.

Finding the GCF of 60, 90 and 120 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 60: 2 × 2 × 3 × 5 (exponent form: 2² × 3 × 5)

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

All Prime Factors of 120: 2 × 2 × 2 × 3 × 5 (exponent form: 2³ × 3 × 5)

Prime factor	60	90	120	Lowest power
2	2²	2	2³	2
3	3	3²	3	3
5	5	5	5	5

GCF = 2 × 3 × 5 = 30

Checking the GCF of 60, 90 and 120 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(60, 90) = 30

GCF(30, 120) = 30

GCF(60, 90, 120) = 30

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

60 ÷ 30 = 2

90 ÷ 30 = 3

120 ÷ 30 = 4

2, 3 and 4 have no common factor left — that is what makes 30 the greatest one.

Related Calculations

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 60, 90 and 120? (The answer is: 30). Enter the first number (e.g. '60'), the second (e.g. '90') and the third (e.g. '120'), 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

GCF Table

Number 1	Number 2	Number 3	GCF
60	90	105	15
60	90	106	2
60	90	107	1
60	90	108	6
60	90	109	1
60	90	110	10
60	90	111	3
60	90	112	2
60	90	113	1
60	90	114	6
60	90	115	5
60	90	116	2
60	90	117	3
60	90	118	2
60	90	119	1
60	90	120	30
60	90	121	1
60	90	122	2
60	90	123	3
60	90	124	2
60	90	125	5
60	90	126	6
60	90	127	1
60	90	128	2
60	90	129	3
60	90	130	10
60	90	131	1
60	90	132	6
60	90	133	1
60	90	134	2

FAQ

What's the Greatest Common Factor (GCF) of 60, 90 and 120?

GCF of 60, 90 and 120 is 30

What prime factors do 60, 90 and 120 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 60, 90 and 120 two numbers at a time?

Yes, and it is the check this page prints. The GCF of 60 and 90 is 30, and the GCF of 30 and 120 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 60 : 90 : 120?

Divide every term by the GCF 30: 60 ÷ 30 = 2, 90 ÷ 30 = 3 and 120 ÷ 30 = 4. So 60 : 90 : 120 in lowest terms is 2 : 3 : 4, and no whole number other than 1 divides all three of those.

GCF for 60, 90 and 120

What's the Greatest Common Factor (GCF) of 60, 90 and 120?

Finding the GCF of 60, 90 and 120 by Prime Factorization

Checking the GCF of 60, 90 and 120 Two Numbers at a Time

Related Calculations

See Also

About "Greatest Common Factor of 3 Numbers" Calculator

GCF Table

FAQ

What's the Greatest Common Factor (GCF) of 60, 90 and 120?

What prime factors do 60, 90 and 120 share?

Can you get the GCF of 60, 90 and 120 two numbers at a time?

How does the GCF simplify the ratio 60 : 90 : 120?

See Also

Number 1	Number 2	Number 3	GCF
60	90	105	15
60	90	106	2
60	90	107	1
60	90	108	6
60	90	109	1
60	90	110	10
60	90	111	3
60	90	112	2
60	90	113	1
60	90	114	6
60	90	115	5
60	90	116	2
60	90	117	3
60	90	118	2
60	90	119	1
60	90	120	30
60	90	121	1
60	90	122	2
60	90	123	3
60	90	124	2
60	90	125	5
60	90	126	6
60	90	127	1
60	90	128	2
60	90	129	3
60	90	130	10
60	90	131	1
60	90	132	6
60	90	133	1
60	90	134	2

Number 1	Number 2	Number 3	GCF
60	90	105	15
60	90	106	2
60	90	107	1
60	90	108	6
60	90	109	1
60	90	110	10
60	90	111	3
60	90	112	2
60	90	113	1
60	90	114	6
60	90	115	5
60	90	116	2
60	90	117	3
60	90	118	2
60	90	119	1
60	90	120	30
60	90	121	1
60	90	122	2
60	90	123	3
60	90	124	2
60	90	125	5
60	90	126	6
60	90	127	1
60	90	128	2
60	90	129	3
60	90	130	10
60	90	131	1
60	90	132	6
60	90	133	1
60	90	134	2

Number 1	Number 2	Number 3	GCF
60	90	105	15
60	90	106	2
60	90	107	1
60	90	108	6
60	90	109	1
60	90	110	10
60	90	111	3
60	90	112	2
60	90	113	1
60	90	114	6
60	90	115	5
60	90	116	2
60	90	117	3
60	90	118	2
60	90	119	1
60	90	120	30
60	90	121	1
60	90	122	2
60	90	123	3
60	90	124	2
60	90	125	5
60	90	126	6
60	90	127	1
60	90	128	2
60	90	129	3
60	90	130	10
60	90	131	1
60	90	132	6
60	90	133	1
60	90	134	2