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GCF for 42, 126 and 210

"Greatest Common Factor of 3 Numbers" Calculator

What's the Greatest Common Factor (GCF) of 42, 126 and 210?

Answer

GCF of 42, 126 and 210 is

(Forty-two)

42 is the largest positive integer that divides 42, 126 and 210 without a remainder — every other common divisor of the three divides it too.

Finding the GCF of 42, 126 and 210 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 42: 2 × 3 × 7 (exponent form: 2 × 3 × 7)

All Prime Factors of 126: 2 × 3 × 3 × 7 (exponent form: 2 × 3² × 7)

All Prime Factors of 210: 2 × 3 × 5 × 7 (exponent form: 2 × 3 × 5 × 7)

Prime factor	42	126	210	Lowest power
2	2	2	2	2
3	3	3²	3	3
5	—	—	5	—
7	7	7	7	7

GCF = 2 × 3 × 7 = 42

Checking the GCF of 42, 126 and 210 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(42, 126) = 42

GCF(42, 210) = 42

GCF(42, 126, 210) = 42

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

42 ÷ 42 = 1

126 ÷ 42 = 3

210 ÷ 42 = 5

1, 3 and 5 have no common factor left — that is what makes 42 the greatest one.

Found an error in the calculation or the information?

Related Calculations

GCF Table

Number 1	Number 2	Number 3	GCF
42	126	195	3
42	126	196	14
42	126	197	1
42	126	198	6
42	126	199	1
42	126	200	2
42	126	201	3
42	126	202	2
42	126	203	7
42	126	204	6
42	126	205	1
42	126	206	2
42	126	207	3
42	126	208	2
42	126	209	1
42	126	210	42
42	126	211	1
42	126	212	2
42	126	213	3
42	126	214	2
42	126	215	1
42	126	216	6
42	126	217	7
42	126	218	2
42	126	219	3
42	126	220	2
42	126	221	1
42	126	222	6
42	126	223	1
42	126	224	14

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 42, 126 and 210? (The answer is: 42). Enter the first number (e.g. '42'), the second (e.g. '126') and the third (e.g. '210'), 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 42, 126 and 210?

GCF of 42, 126 and 210 is 42

What prime factors do 42, 126 and 210 share?

All three factorizations contain 2 × 3 × 7, and multiplying those shared primes gives 42 — exactly the greatest common factor.

Can you get the GCF of 42, 126 and 210 two numbers at a time?

Yes, and it is the check this page prints. The GCF of 42 and 126 is 42, and the GCF of 42 and 210 is 42 — 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 42 : 126 : 210?

Divide every term by the GCF 42: 42 ÷ 42 = 1, 126 ÷ 42 = 3 and 210 ÷ 42 = 5. So 42 : 126 : 210 in lowest terms is 1 : 3 : 5, and no whole number other than 1 divides all three of those.

GCF for 42, 126 and 210

What's the Greatest Common Factor (GCF) of 42, 126 and 210?

Finding the GCF of 42, 126 and 210 by Prime Factorization

Checking the GCF of 42, 126 and 210 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 42, 126 and 210?

What prime factors do 42, 126 and 210 share?

Can you get the GCF of 42, 126 and 210 two numbers at a time?

How does the GCF simplify the ratio 42 : 126 : 210?

See Also

Number 1	Number 2	Number 3	GCF
42	126	195	3
42	126	196	14
42	126	197	1
42	126	198	6
42	126	199	1
42	126	200	2
42	126	201	3
42	126	202	2
42	126	203	7
42	126	204	6
42	126	205	1
42	126	206	2
42	126	207	3
42	126	208	2
42	126	209	1
42	126	210	42
42	126	211	1
42	126	212	2
42	126	213	3
42	126	214	2
42	126	215	1
42	126	216	6
42	126	217	7
42	126	218	2
42	126	219	3
42	126	220	2
42	126	221	1
42	126	222	6
42	126	223	1
42	126	224	14

Number 1	Number 2	Number 3	GCF
42	126	195	3
42	126	196	14
42	126	197	1
42	126	198	6
42	126	199	1
42	126	200	2
42	126	201	3
42	126	202	2
42	126	203	7
42	126	204	6
42	126	205	1
42	126	206	2
42	126	207	3
42	126	208	2
42	126	209	1
42	126	210	42
42	126	211	1
42	126	212	2
42	126	213	3
42	126	214	2
42	126	215	1
42	126	216	6
42	126	217	7
42	126	218	2
42	126	219	3
42	126	220	2
42	126	221	1
42	126	222	6
42	126	223	1
42	126	224	14

Number 1	Number 2	Number 3	GCF
42	126	195	3
42	126	196	14
42	126	197	1
42	126	198	6
42	126	199	1
42	126	200	2
42	126	201	3
42	126	202	2
42	126	203	7
42	126	204	6
42	126	205	1
42	126	206	2
42	126	207	3
42	126	208	2
42	126	209	1
42	126	210	42
42	126	211	1
42	126	212	2
42	126	213	3
42	126	214	2
42	126	215	1
42	126	216	6
42	126	217	7
42	126	218	2
42	126	219	3
42	126	220	2
42	126	221	1
42	126	222	6
42	126	223	1
42	126	224	14