Greatest Common Factor of 68/45, 38/19, 52/21, 31/11

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

GCF of 68/45, 38/19, 52/21, 31/11

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 68/45,38/19,52/21,31/11

Given fractions are 68/45,38/19,52/21,31/11

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 68,38,52,31

Greatest Common Factor of Numerators i.e. GCF of 68,38,52,31 is 1 .

LCM of Denominators means LCM of 45,19,21,11 as per the given fractions.

LCM of 45,19,21,11 is 65835 as it is the smallest common factor for both these numbers.

Lets's calculate GCF of 68,38,52,31

GCF of Fractions 68/45,38/19,52/21,31/11 is 1/65835

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

Greatest Common Factor of 68,38,52,31 By Matching Biggest Common Factor Method

Greatest Common Factor of 68,38,52,31 By Matching Biggest Common Factor Method

Factors of 68

List of positive integer factors of 68 that divides 68 without a remainder.

1,2,4,17,34,68

Factors of 38

List of positive integer factors of 38 that divides 38 without a remainder.

1,2,19,38

Factors of 52

List of positive integer factors of 52 that divides 52 without a remainder.

1,2,4,13,26,52

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 68,38,52,31 . The biggest common factor number is the GCF number.
So the greatest common factor 68,38,52,31 is 1.

Lets's calculate LCM of 45,19,21,11

3 45, 19, 21, 11
15, 19, 7, 11

∴ So the LCM of the given numbers is 3 x 15 x 19 x 7 x 11 = 65835

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/65835

Therefore, the GCF of Fractions 68/45,38/19,52/21,31/11 is 1/65835

Least Common Multiple of 45,19,21,11 with GCF Formula

Least Common Multiple of 45,19,21,11 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 45,19,21,11 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(45,19,21,11) = 1

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

GCF(45,19,21,11) x common factors =1 x 3 = 3

LCM(45,19,21,11) = ( 45 × 19 × 21 × 11 ) / 3

LCM(45,19,21,11) = 197505 / 3

LCM(45,19,21,11) = 65835


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 68/45, 38/19, 52/21, 31/11

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 68/45, 38/19, 52/21, 31/11?

Answer: GCF of Numerators as per given numbers 68/45, 38/19, 52/21, 31/11 is

GCF of Numerators i.e. for 68,38,52,31 is 1

LCM of denominators i.e. for 45,19,21,11 is 65835.

Thus, GCF of Fractions is 1/65835.Finally, GCF of Fractions for 68/45, 38/19, 52/21, 31/11 is 1/65835.