Greatest Common Factor of 19/31, 16/61, 61/57, 20/78

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

GCF of 19/31, 16/61, 61/57, 20/78

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 19/31,16/61,61/57,20/78

Given fractions are 19/31,16/61,61/57,20/78

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 19,16,61,20

Greatest Common Factor of Numerators i.e. GCF of 19,16,61,20 is 1 .

LCM of Denominators means LCM of 31,61,57,78 as per the given fractions.

LCM of 31,61,57,78 is 2802462 as it is the smallest common factor for both these numbers.

Lets's calculate GCF of 19,16,61,20

GCF of Fractions 19/31,16/61,61/57,20/78 is 1/2802462

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

Greatest Common Factor of 19,16,61,20 By Matching Biggest Common Factor Method

Greatest Common Factor of 19,16,61,20 By Matching Biggest Common Factor Method

Factors of 19

List of positive integer factors of 19 that divides 19 without a remainder.

1,19

Factors of 16

List of positive integer factors of 16 that divides 16 without a remainder.

1,2,4,8,16

Factors of 61

List of positive integer factors of 61 that divides 61 without a remainder.

1,61

Factors of 20

List of positive integer factors of 20 that divides 20 without a remainder.

1,2,4,5,10,20

Greatest Common Factor

We found the factors 19,16,61,20 . The biggest common factor number is the GCF number.
So the greatest common factor 19,16,61,20 is 1.

Lets's calculate LCM of 31,61,57,78

3 31, 61, 57, 78
31, 61, 19, 26

∴ So the LCM of the given numbers is 3 x 31 x 61 x 19 x 26 = 2802462

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/2802462

Therefore, the GCF of Fractions 19/31,16/61,61/57,20/78 is 1/2802462

Least Common Multiple of 31,61,57,78 with GCF Formula

Least Common Multiple of 31,61,57,78 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 31,61,57,78 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(31,61,57,78) = 1

common factors(in case of two or more numbers have common factors) = 3

GCF(31,61,57,78) x common factors =1 x 3 = 3

LCM(31,61,57,78) = ( 31 × 61 × 57 × 78 ) / 3

LCM(31,61,57,78) = 8407386 / 3

LCM(31,61,57,78) = 2802462


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 19/31, 16/61, 61/57, 20/78

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 19/31, 16/61, 61/57, 20/78?

Answer: GCF of Numerators as per given numbers 19/31, 16/61, 61/57, 20/78 is

GCF of Numerators i.e. for 19,16,61,20 is 1

LCM of denominators i.e. for 31,61,57,78 is 2802462.

Thus, GCF of Fractions is 1/2802462.Finally, GCF of Fractions for 19/31, 16/61, 61/57, 20/78 is 1/2802462.