Greatest Common Factor of 78/65, 86/65, 49/38, 23/31

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

GCF of 78/65, 86/65, 49/38, 23/31

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 78/65,86/65,49/38,23/31

Given fractions are 78/65,86/65,49/38,23/31

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 78,86,49,23

Greatest Common Factor of Numerators i.e. GCF of 78,86,49,23 is 1 .

LCM of Denominators means LCM of 65,65,38,31 as per the given fractions.

LCM of 65,65,38,31 is 76570 as it is the smallest common factor for both these numbers.

Lets's calculate GCF of 78,86,49,23

GCF of Fractions 78/65,86/65,49/38,23/31 is 1/76570

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

Greatest Common Factor of 78,86,49,23 By Matching Biggest Common Factor Method

Greatest Common Factor of 78,86,49,23 By Matching Biggest Common Factor Method

Factors of 78

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

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

Factors of 86

List of positive integer factors of 86 that divides 86 without a remainder.

1,2,43,86

Factors of 49

List of positive integer factors of 49 that divides 49 without a remainder.

1,7,49

Factors of 23

List of positive integer factors of 23 that divides 23 without a remainder.

1,23

Greatest Common Factor

We found the factors 78,86,49,23 . The biggest common factor number is the GCF number.
So the greatest common factor 78,86,49,23 is 1.

Lets's calculate LCM of 65,65,38,31

5 65, 65, 38, 31
13 13, 13, 38, 31
1, 1, 38, 31

∴ So the LCM of the given numbers is 5 x 13 x 1 x 1 x 38 x 31 = 76570

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/76570

Therefore, the GCF of Fractions 78/65,86/65,49/38,23/31 is 1/76570

Least Common Multiple of 65,65,38,31 with GCF Formula

Least Common Multiple of 65,65,38,31 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 65,65,38,31 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(65,65,38,31) = 1

common factors(in case of two or more numbers have common factors) = 65

GCF(65,65,38,31) x common factors =1 x 65 = 65

LCM(65,65,38,31) = ( 65 × 65 × 38 × 31 ) / 65

LCM(65,65,38,31) = 4977050 / 65

LCM(65,65,38,31) = 76570


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 78/65, 86/65, 49/38, 23/31

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 78/65, 86/65, 49/38, 23/31?

Answer: GCF of Numerators as per given numbers 78/65, 86/65, 49/38, 23/31 is

GCF of Numerators i.e. for 78,86,49,23 is 1

LCM of denominators i.e. for 65,65,38,31 is 76570.

Thus, GCF of Fractions is 1/76570.Finally, GCF of Fractions for 78/65, 86/65, 49/38, 23/31 is 1/76570.