Greatest Common Factor of 21/106, 59/314, 111/204

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

GCF of 21/106, 59/314, 111/204

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 21/106,59/314,111/204

Given fractions are 21/106,59/314,111/204

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 21,59,111

Greatest Common Factor of Numerators i.e. GCF of 21,59,111 is 1 .

LCM of Denominators means LCM of 106,314,204 as per the given fractions.

LCM of 106,314,204 is 1697484 as it is the smallest common factor for both these numbers.

Lets's calculate GCF of 21,59,111

GCF of Fractions 21/106,59/314,111/204 is 1/1697484

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

Greatest Common Factor of 21,59,111 By Matching Biggest Common Factor Method

Greatest Common Factor of 21,59,111 By Matching Biggest Common Factor Method

Factors of 21

List of positive integer factors of 21 that divides 21 without a remainder.

1,3,7,21

Factors of 59

List of positive integer factors of 59 that divides 59 without a remainder.

1,59

Factors of 111

List of positive integer factors of 111 that divides 111 without a remainder.

1,3,37,111

Greatest Common Factor

We found the factors 21,59,111 . The biggest common factor number is the GCF number.
So the greatest common factor 21,59,111 is 1.

Lets's calculate LCM of 106,314,204

2 106, 314, 204
53, 157, 102

∴ So the LCM of the given numbers is 2 x 53 x 157 x 102 = 1697484

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/1697484

Therefore, the GCF of Fractions 21/106,59/314,111/204 is 1/1697484

Least Common Multiple of 106,314,204 with GCF Formula

Least Common Multiple of 106,314,204 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 106,314,204 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(106,314,204) = 2

common factors(in case of two or more numbers have common factors) = 2

GCF(106,314,204) x common factors =2 x 2 = 4

LCM(106,314,204) = ( 106 × 314 × 204 ) / 4

LCM(106,314,204) = 6789936 / 4

LCM(106,314,204) = 1697484


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 21/106, 59/314, 111/204

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 21/106, 59/314, 111/204?

Answer: GCF of Numerators as per given numbers 21/106, 59/314, 111/204 is

GCF of Numerators i.e. for 21,59,111 is 1

LCM of denominators i.e. for 106,314,204 is 1697484.

Thus, GCF of Fractions is 1/1697484.Finally, GCF of Fractions for 21/106, 59/314, 111/204 is 1/1697484.