Greatest Common Factor of 34/20, 72/68, 35/56, 12/21

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

GCF of 34/20, 72/68, 35/56, 12/21

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 34/20,72/68,35/56,12/21

Given fractions are 34/20,72/68,35/56,12/21

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 34,72,35,12

Greatest Common Factor of Numerators i.e. GCF of 34,72,35,12 is 1 .

LCM of Denominators means LCM of 20,68,56,21 as per the given fractions.

LCM of 20,68,56,21 is 14280 as it is the smallest common factor for both these numbers.

Lets's calculate GCF of 34,72,35,12

GCF of Fractions 34/20,72/68,35/56,12/21 is 1/14280

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

Greatest Common Factor of 34,72,35,12 By Matching Biggest Common Factor Method

Greatest Common Factor of 34,72,35,12 By Matching Biggest Common Factor Method

Factors of 34

List of positive integer factors of 34 that divides 34 without a remainder.

1,2,17,34

Factors of 72

List of positive integer factors of 72 that divides 72 without a remainder.

1,2,3,4,6,8,9,12,18,24,36,72

Factors of 35

List of positive integer factors of 35 that divides 35 without a remainder.

1,5,7,35

Factors of 12

List of positive integer factors of 12 that divides 12 without a remainder.

1,2,3,4,6,12

Greatest Common Factor

We found the factors 34,72,35,12 . The biggest common factor number is the GCF number.
So the greatest common factor 34,72,35,12 is 1.

Lets's calculate LCM of 20,68,56,21

2 20, 68, 56, 21
2 10, 34, 28, 21
7 5, 17, 14, 21
5, 17, 2, 3

∴ So the LCM of the given numbers is 2 x 2 x 7 x 5 x 17 x 2 x 3 = 14280

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/14280

Therefore, the GCF of Fractions 34/20,72/68,35/56,12/21 is 1/14280

Least Common Multiple of 20,68,56,21 with GCF Formula

Least Common Multiple of 20,68,56,21 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 20,68,56,21 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(20,68,56,21) = 1

common factors(in case of two or more numbers have common factors) = 112

GCF(20,68,56,21) x common factors =1 x 112 = 112

LCM(20,68,56,21) = ( 20 × 68 × 56 × 21 ) / 112

LCM(20,68,56,21) = 1599360 / 112

LCM(20,68,56,21) = 14280


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 34/20, 72/68, 35/56, 12/21

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 34/20, 72/68, 35/56, 12/21?

Answer: GCF of Numerators as per given numbers 34/20, 72/68, 35/56, 12/21 is

GCF of Numerators i.e. for 34,72,35,12 is 1

LCM of denominators i.e. for 20,68,56,21 is 14280.

Thus, GCF of Fractions is 1/14280.Finally, GCF of Fractions for 34/20, 72/68, 35/56, 12/21 is 1/14280.