Greatest Common Factor of 77/70, 31/90, 35/21, 78/686

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

GCF of 77/70, 31/90, 35/21, 78/686

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 77/70,31/90,35/21,78/686

Given fractions are 77/70,31/90,35/21,78/686

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 77,31,35,78

Greatest Common Factor of Numerators i.e. GCF of 77,31,35,78 is 1 .

LCM of Denominators means LCM of 70,90,21,686 as per the given fractions.

LCM of 70,90,21,686 is 30870 as it is the smallest common factor for both these numbers.

Lets's calculate GCF of 77,31,35,78

GCF of Fractions 77/70,31/90,35/21,78/686 is 1/30870

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

Greatest Common Factor of 77,31,35,78 By Matching Biggest Common Factor Method

Greatest Common Factor of 77,31,35,78 By Matching Biggest Common Factor Method

Factors of 77

List of positive integer factors of 77 that divides 77 without a remainder.

1,7,11,77

Factors of 31

List of positive integer factors of 31 that divides 31 without a remainder.

1,31

Factors of 35

List of positive integer factors of 35 that divides 35 without a remainder.

1,5,7,35

Factors of 78

List of positive integer factors of 78 that divides 78 without a remainder.

1,2,3,6,13,26,39,78

Greatest Common Factor

We found the factors 77,31,35,78 . The biggest common factor number is the GCF number.
So the greatest common factor 77,31,35,78 is 1.

Lets's calculate LCM of 70,90,21,686

2 70, 90, 21, 686
3 35, 45, 21, 343
5 35, 15, 7, 343
7 7, 3, 7, 343
1, 3, 1, 49

∴ So the LCM of the given numbers is 2 x 3 x 5 x 7 x 1 x 3 x 1 x 49 = 30870

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/30870

Therefore, the GCF of Fractions 77/70,31/90,35/21,78/686 is 1/30870

Least Common Multiple of 70,90,21,686 with GCF Formula

Least Common Multiple of 70,90,21,686 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 70,90,21,686 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(70,90,21,686) = 1

common factors(in case of two or more numbers have common factors) = 2940

GCF(70,90,21,686) x common factors =1 x 2940 = 2940

LCM(70,90,21,686) = ( 70 × 90 × 21 × 686 ) / 2940

LCM(70,90,21,686) = 90757800 / 2940

LCM(70,90,21,686) = 30870


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 77/70, 31/90, 35/21, 78/686

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 77/70, 31/90, 35/21, 78/686?

Answer: GCF of Numerators as per given numbers 77/70, 31/90, 35/21, 78/686 is

GCF of Numerators i.e. for 77,31,35,78 is 1

LCM of denominators i.e. for 70,90,21,686 is 30870.

Thus, GCF of Fractions is 1/30870.Finally, GCF of Fractions for 77/70, 31/90, 35/21, 78/686 is 1/30870.