Greatest Common Factor of 43/14, 75/21, 80/71

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

GCF of 43/14, 75/21, 80/71

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 43/14,75/21,80/71

Given fractions are 43/14,75/21,80/71

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 43,75,80

Greatest Common Factor of Numerators i.e. GCF of 43,75,80 is 1 .

LCM of Denominators means LCM of 14,21,71 as per the given fractions.

LCM of 14,21,71 is 2982 as it is the smallest common factor for both these numbers.

Lets's calculate GCF of 43,75,80

GCF of Fractions 43/14,75/21,80/71 is 1/2982

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

Greatest Common Factor of 43,75,80 By Matching Biggest Common Factor Method

Greatest Common Factor of 43,75,80 By Matching Biggest Common Factor Method

Factors of 43

List of positive integer factors of 43 that divides 43 without a remainder.

1,43

Factors of 75

List of positive integer factors of 75 that divides 75 without a remainder.

1,3,5,15,25,75

Factors of 80

List of positive integer factors of 80 that divides 80 without a remainder.

1,2,4,5,8,10,16,20,40,80

Greatest Common Factor

We found the factors 43,75,80 . The biggest common factor number is the GCF number.
So the greatest common factor 43,75,80 is 1.

Lets's calculate LCM of 14,21,71

7 14, 21, 71
2, 3, 71

∴ So the LCM of the given numbers is 7 x 2 x 3 x 71 = 2982

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/2982

Therefore, the GCF of Fractions 43/14,75/21,80/71 is 1/2982

Least Common Multiple of 14,21,71 with GCF Formula

Least Common Multiple of 14,21,71 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 14,21,71 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(14,21,71) = 1

common factors(in case of two or more numbers have common factors) = 7

GCF(14,21,71) x common factors =1 x 7 = 7

LCM(14,21,71) = ( 14 × 21 × 71 ) / 7

LCM(14,21,71) = 20874 / 7

LCM(14,21,71) = 2982


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 43/14, 75/21, 80/71

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 43/14, 75/21, 80/71?

Answer: GCF of Numerators as per given numbers 43/14, 75/21, 80/71 is

GCF of Numerators i.e. for 43,75,80 is 1

LCM of denominators i.e. for 14,21,71 is 2982.

Thus, GCF of Fractions is 1/2982.Finally, GCF of Fractions for 43/14, 75/21, 80/71 is 1/2982.