Greatest Common Factor of 31/75, 78/80, 73/54, 83/459

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

GCF of 31/75, 78/80, 73/54, 83/459

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 31/75,78/80,73/54,83/459

Given fractions are 31/75,78/80,73/54,83/459

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 31,78,73,83

Greatest Common Factor of Numerators i.e. GCF of 31,78,73,83 is 1 .

LCM of Denominators means LCM of 75,80,54,459 as per the given fractions.

LCM of 75,80,54,459 is 183600 as it is the smallest common factor for both these numbers.

Lets's calculate GCF of 31,78,73,83

GCF of Fractions 31/75,78/80,73/54,83/459 is 1/183600

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

Greatest Common Factor of 31,78,73,83 By Matching Biggest Common Factor Method

Greatest Common Factor of 31,78,73,83 By Matching Biggest Common Factor Method

Factors of 31

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

1,31

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 73

List of positive integer factors of 73 that divides 73 without a remainder.

1,73

Factors of 83

List of positive integer factors of 83 that divides 83 without a remainder.

1,83

Greatest Common Factor

We found the factors 31,78,73,83 . The biggest common factor number is the GCF number.
So the greatest common factor 31,78,73,83 is 1.

Lets's calculate LCM of 75,80,54,459

2 75, 80, 54, 459
3 75, 40, 27, 459
3 25, 40, 9, 153
3 25, 40, 3, 51
5 25, 40, 1, 17
5, 8, 1, 17

∴ So the LCM of the given numbers is 2 x 3 x 3 x 3 x 5 x 5 x 8 x 1 x 17 = 183600

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/183600

Therefore, the GCF of Fractions 31/75,78/80,73/54,83/459 is 1/183600

Least Common Multiple of 75,80,54,459 with GCF Formula

Least Common Multiple of 75,80,54,459 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 75,80,54,459 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(75,80,54,459) = 1

common factors(in case of two or more numbers have common factors) = 810

GCF(75,80,54,459) x common factors =1 x 810 = 810

LCM(75,80,54,459) = ( 75 × 80 × 54 × 459 ) / 810

LCM(75,80,54,459) = 148716000 / 810

LCM(75,80,54,459) = 183600


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 31/75, 78/80, 73/54, 83/459

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 31/75, 78/80, 73/54, 83/459?

Answer: GCF of Numerators as per given numbers 31/75, 78/80, 73/54, 83/459 is

GCF of Numerators i.e. for 31,78,73,83 is 1

LCM of denominators i.e. for 75,80,54,459 is 183600.

Thus, GCF of Fractions is 1/183600.Finally, GCF of Fractions for 31/75, 78/80, 73/54, 83/459 is 1/183600.