Greatest Common Factor of 6/14, 702/31, 734/77

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

GCF of 6/14, 702/31, 734/77

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 6/14,702/31,734/77

Given fractions are 6/14,702/31,734/77

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 6,702,734

Greatest Common Factor of Numerators i.e. GCF of 6,702,734 is 2 .

LCM of Denominators means LCM of 14,31,77 as per the given fractions.

LCM of 14,31,77 is 4774 as it is the smallest common factor for both these numbers.

Lets's calculate GCF of 6,702,734

GCF of Fractions 6/14,702/31,734/77 is 2/4774

2 6, 702, 734
3, 351, 367

∴ So the GCF of the given numbers is 2 = 2

Greatest Common Factor of 6,702,734 By Matching Biggest Common Factor Method

Greatest Common Factor of 6,702,734 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 702

List of positive integer factors of 702 that divides 702 without a remainder.

1,2,3,6,9,13,18,26,27,39,54,78,117,234,351,702

Factors of 734

List of positive integer factors of 734 that divides 734 without a remainder.

1,2,367,734

Greatest Common Factor

We found the factors 6,702,734 . The biggest common factor number is the GCF number.
So the greatest common factor 6,702,734 is 2.

Lets's calculate LCM of 14,31,77

7 14, 31, 77
2, 31, 11

∴ So the LCM of the given numbers is 7 x 2 x 31 x 11 = 4774

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/4774

Therefore, the GCF of Fractions 6/14,702/31,734/77 is 2/4774

Least Common Multiple of 14,31,77 with GCF Formula

Least Common Multiple of 14,31,77 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 14,31,77 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(14,31,77) = 1

common factors(in case of two or more numbers have common factors) = 7

GCF(14,31,77) x common factors =1 x 7 = 7

LCM(14,31,77) = ( 14 × 31 × 77 ) / 7

LCM(14,31,77) = 33418 / 7

LCM(14,31,77) = 4774


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 6/14, 702/31, 734/77

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 6/14, 702/31, 734/77?

Answer: GCF of Numerators as per given numbers 6/14, 702/31, 734/77 is

GCF of Numerators i.e. for 6,702,734 is 2

LCM of denominators i.e. for 14,31,77 is 4774.

Thus, GCF of Fractions is 2/4774.Finally, GCF of Fractions for 6/14, 702/31, 734/77 is 2/4774.