Greatest Common Factor of 6/42, 12/78, 80/520, 309/696

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

GCF of 6/42, 12/78, 80/520, 309/696

Enter two or more fractions separated by "commas"

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

GCF of:

Greatest Common Factor of 6/42,12/78,80/520,309/696

Given fractions are 6/42,12/78,80/520,309/696

Formula to find GCF of Fractions is

GCF = GCF of Numerators/LCM of Denominators

As per the formula GCF of Fractions let’s split into two parts and find the GCF of Numerators and LCM of Denominators

In the given fractions GCF of Numerators means GCF of 6,12,80,309

Greatest Common Factor of Numerators i.e. GCF of 6,12,80,309 is 1 .

LCM of Denominators means LCM of 42,78,520,696 as per the given fractions.

LCM of 42,78,520,696 is 316680 as it is the smallest common factor for both these numbers.

Lets's calculate GCF of 6,12,80,309

GCF of Fractions 6/42,12/78,80/520,309/696 is 1/316680

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

Greatest Common Factor of 6,12,80,309 By Matching Biggest Common Factor Method

Greatest Common Factor of 6,12,80,309 By Matching Biggest Common Factor Method

Factors of 6

List of positive integer factors of 6 that divides 6 without a remainder.

1,2,3,6

Factors of 12

List of positive integer factors of 12 that divides 12 without a remainder.

1,2,3,4,6,12

Factors of 80

List of positive integer factors of 80 that divides 80 without a remainder.

1,2,4,5,8,10,16,20,40,80

Factors of 309

List of positive integer factors of 309 that divides 309 without a remainder.

1,3,103,309

Greatest Common Factor

We found the factors 6,12,80,309 . The biggest common factor number is the GCF number.
So the greatest common factor 6,12,80,309 is 1.

Lets's calculate LCM of 42,78,520,696

2 42, 78, 520, 696
2 21, 39, 260, 348
2 21, 39, 130, 174
3 21, 39, 65, 87
13 7, 13, 65, 29
7, 1, 5, 29

∴ So the LCM of the given numbers is 2 x 2 x 2 x 3 x 13 x 7 x 1 x 5 x 29 = 316680

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/316680

Therefore, the GCF of Fractions 6/42,12/78,80/520,309/696 is 1/316680

Least Common Multiple of 42,78,520,696 with GCF Formula

Least Common Multiple of 42,78,520,696 with GCF Formula

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

We need to calculate greatest common factor of 42,78,520,696 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(42,78,520,696) = 2

common factors(in case of two or more numbers have common factors) = 1872

GCF(42,78,520,696) x common factors =2 x 1872 = 3744

LCM(42,78,520,696) = ( 42 × 78 × 520 × 696 ) / 3744

LCM(42,78,520,696) = 1185649920 / 3744

LCM(42,78,520,696) = 316680


GCF of Fractions Calculation Examples

Here are some samples of GCF of Fractions calculations.

GCF of Fractions Calculation Examples

Here are some samples of GCF of Fractions calculations.

Frequently Asked Questions on Fractional GCF of 6/42, 12/78, 80/520, 309/696

1. 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.

2. What is the GCF of Fractions for 6/42, 12/78, 80/520, 309/696?

Answer: GCF of Numerators as per given numbers 6/42, 12/78, 80/520, 309/696 is

GCF of Numerators i.e. for 6,12,80,309 is 1

LCM of denominators i.e. for 42,78,520,696 is 316680.

Thus, GCF of Fractions is 1/316680.Finally, GCF of Fractions for 6/42, 12/78, 80/520, 309/696 is 1/316680.