Greatest Common Factor of 30/24, 75/20, 76/49, 31/49

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

GCF of 30/24, 75/20, 76/49, 31/49

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 30/24,75/20,76/49,31/49

Given fractions are 30/24,75/20,76/49,31/49

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 30,75,76,31

Greatest Common Factor of Numerators i.e. GCF of 30,75,76,31 is 1 .

LCM of Denominators means LCM of 24,20,49,49 as per the given fractions.

LCM of 24,20,49,49 is 5880 as it is the smallest common factor for both these numbers.

Lets's calculate GCF of 30,75,76,31

GCF of Fractions 30/24,75/20,76/49,31/49 is 1/5880

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

Greatest Common Factor of 30,75,76,31 By Matching Biggest Common Factor Method

Greatest Common Factor of 30,75,76,31 By Matching Biggest Common Factor Method

Factors of 30

List of positive integer factors of 30 that divides 30 without a remainder.

1,2,3,5,6,10,15,30

Factors of 75

List of positive integer factors of 75 that divides 75 without a remainder.

1,3,5,15,25,75

Factors of 76

List of positive integer factors of 76 that divides 76 without a remainder.

1,2,4,19,38,76

Factors of 31

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

1,31

Greatest Common Factor

We found the factors 30,75,76,31 . The biggest common factor number is the GCF number.
So the greatest common factor 30,75,76,31 is 1.

Lets's calculate LCM of 24,20,49,49

2 24, 20, 49, 49
2 12, 10, 49, 49
7 6, 5, 49, 49
7 6, 5, 7, 7
6, 5, 1, 1

∴ So the LCM of the given numbers is 2 x 2 x 7 x 7 x 6 x 5 x 1 x 1 = 5880

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/5880

Therefore, the GCF of Fractions 30/24,75/20,76/49,31/49 is 1/5880

Least Common Multiple of 24,20,49,49 with GCF Formula

Least Common Multiple of 24,20,49,49 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 24,20,49,49 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(24,20,49,49) = 1

common factors(in case of two or more numbers have common factors) = 196

GCF(24,20,49,49) x common factors =1 x 196 = 196

LCM(24,20,49,49) = ( 24 × 20 × 49 × 49 ) / 196

LCM(24,20,49,49) = 1152480 / 196

LCM(24,20,49,49) = 5880


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 30/24, 75/20, 76/49, 31/49

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 30/24, 75/20, 76/49, 31/49?

Answer: GCF of Numerators as per given numbers 30/24, 75/20, 76/49, 31/49 is

GCF of Numerators i.e. for 30,75,76,31 is 1

LCM of denominators i.e. for 24,20,49,49 is 5880.

Thus, GCF of Fractions is 1/5880.Finally, GCF of Fractions for 30/24, 75/20, 76/49, 31/49 is 1/5880.