Greatest Common Factor of 49/23, 77/31, 39/28, 65/109

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

GCF of 49/23, 77/31, 39/28, 65/109

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 49/23,77/31,39/28,65/109

Given fractions are 49/23,77/31,39/28,65/109

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 49,77,39,65

Greatest Common Factor of Numerators i.e. GCF of 49,77,39,65 is 1 .

LCM of Denominators means LCM of 23,31,28,109 as per the given fractions.

LCM of 23,31,28,109 is 2176076 as it is the smallest common factor for both these numbers.

Lets's calculate GCF of 49,77,39,65

GCF of Fractions 49/23,77/31,39/28,65/109 is 1/2176076

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

Greatest Common Factor of 49,77,39,65 By Matching Biggest Common Factor Method

Greatest Common Factor of 49,77,39,65 By Matching Biggest Common Factor Method

Factors of 49

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

1,7,49

Factors of 77

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

1,7,11,77

Factors of 39

List of positive integer factors of 39 that divides 39 without a remainder.

1,3,13,39

Factors of 65

List of positive integer factors of 65 that divides 65 without a remainder.

1,5,13,65

Greatest Common Factor

We found the factors 49,77,39,65 . The biggest common factor number is the GCF number.
So the greatest common factor 49,77,39,65 is 1.

Lets's calculate LCM of 23,31,28,109

Given numbers has no common factors except 1. So, there LCM is their product i.e 2176076

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/2176076

Therefore, the GCF of Fractions 49/23,77/31,39/28,65/109 is 1/2176076

Least Common Multiple of 23,31,28,109 with GCF Formula

Least Common Multiple of 23,31,28,109 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 23,31,28,109 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(23,31,28,109) = 1

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

GCF(23,31,28,109) x common factors =1 x 1 = 1

LCM(23,31,28,109) = ( 23 × 31 × 28 × 109 ) / 1

LCM(23,31,28,109) = 2176076 / 1

LCM(23,31,28,109) = 2176076


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 49/23, 77/31, 39/28, 65/109

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 49/23, 77/31, 39/28, 65/109?

Answer: GCF of Numerators as per given numbers 49/23, 77/31, 39/28, 65/109 is

GCF of Numerators i.e. for 49,77,39,65 is 1

LCM of denominators i.e. for 23,31,28,109 is 2176076.

Thus, GCF of Fractions is 1/2176076.Finally, GCF of Fractions for 49/23, 77/31, 39/28, 65/109 is 1/2176076.