How to Find GCF of 684/626, 131/978?

GCF of 684/626, 131/978

Created By : Veerendra
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023

Use our free GCF of Fractions Calculator tool to compute the GCF of 684/626, 131/978 i.e 1/306114 easily. The following is the detailed procedure to determine the greatest common factor of fractions 684/626, 131/978.

Enter two or more fractions separated by "commas"

Ex: 2/3, 5/7 or 3/5, 5/9, 7/3

What is the GCF of 684/626,131/978?

Given fractions are 684/626,131/978

To find the GCF of fractions, we have to find the GCF of numerator numbers and LCM of denominator numbers. Its formula is given by

GCF of Fraction = Greatest Common Factor of Numerator/Least Common Multiple of Denominators

In the fractions 684/626,131/978, numerators are 684,131

Denominators are 626,978

The GCF of 684,131 is 1 .

LCM of 626,978 is 306114.

The greatest common factor of 684/626,131/978 = [GCF of 684,131]/[LCM of 626,978]= 1/306114

Therefore, the GCF of 684/626,131/978 is 1/306114.

Greatest Common Factor of 684,131

To find the highest common factor of 684,131, we have to find the factors of both numbers and list the highest common factor.

The factors of 684 are 1, 2, 3, 4, 6, 9, 12, 18, 19, 36, 38, 57, 76, 114, 171, 228, 342, 684

The factors of 131 are 1, 131

The HCF of 684,131 is 1.

Lets's calculate GCF of 684,131

Greatest Common Factor (GCF) of 684,131 By Common Division

∴ So GCF of numbers is 1 because of no common factors present between them.

Greatest Common Factor of 684,131 By Matching Biggest Common Factor Method

Now, list down the factors of 684

1,2,3,4,6,9,12,18,19,36,38,57,76,114,171,228,342,684

Now, list down the factors of 131

1,131

Greatest Common Factor

We found the factors 684,131 . The biggest common factor number is the GCF number.
So the greatest common factor 684,131 is 1.

Lets's calculate LCM of 626,978

Lowest Common Multiple of 626,978 using Common Division

2	626, 978
	313, 489

∴ So the LCM of the given numbers is 2 x 313 x 489 = 306114

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/306114

Therefore, the GCF of Fractions 684/626,131/978 is 1/306114

Least Common Multiple of 626,978 with GCF Formula

The formula of LCM is LCM(a₁,a₂,a₃....,a_n) = ( a₁ × a₂ × a₃ × .... × a_n) / GCF(a₁,a₂,a₃....,a_n) x common factors(if more than 2 numbers have common factors).

We need to calculate greatest common factor of 626,978 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(626,978) = 2

common factors(in case of two or more numbers have common factors) = 1

GCF(626,978) x common factors =2 x 1 = 2

LCM(626,978) = ( 626 × 978 ) / 2

LCM(626,978) = 612228 / 2

LCM(626,978) = 306114

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FAQs on GCF of Fractions of 684/626, 131/978

1. What is the HCF of 684,131?

The HCF of 684,131 is 1

2. What is the GCF of a fraction?

The GCF of a fraction is defined as the greatest fraction that divides exactly into 2 or more fractions.

3. How to find GCF in Fractions?

Answer: GCF of fractions can be found using the simple formula GCF of Fractions = GCF of Numerators/LCM of Denominators.

4. What is the GCF of Fractions for 684/626, 131/978?

Answer: GCF of Numerators as per given numbers 684/626, 131/978 is

GCF of Numerators i.e. for 684,131 is 1

LCM of denominators i.e. for 626,978 is 306114.

Thus, GCF of Fractions is 1/306114.Finally, GCF of Fractions for 684/626, 131/978 is 1/306114.