Greatest Common Factor of 86/13, 84/54, 20/24, 75/342

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

GCF of 86/13, 84/54, 20/24, 75/342

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 86/13,84/54,20/24,75/342

Given fractions are 86/13,84/54,20/24,75/342

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 86,84,20,75

Greatest Common Factor of Numerators i.e. GCF of 86,84,20,75 is 1 .

LCM of Denominators means LCM of 13,54,24,342 as per the given fractions.

LCM of 13,54,24,342 is 53352 as it is the smallest common factor for both these numbers.

Lets's calculate GCF of 86,84,20,75

GCF of Fractions 86/13,84/54,20/24,75/342 is 1/53352

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

Greatest Common Factor of 86,84,20,75 By Matching Biggest Common Factor Method

Greatest Common Factor of 86,84,20,75 By Matching Biggest Common Factor Method

Factors of 86

List of positive integer factors of 86 that divides 86 without a remainder.

1,2,43,86

Factors of 84

List of positive integer factors of 84 that divides 84 without a remainder.

1,2,3,4,6,7,12,14,21,28,42,84

Factors of 20

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

1,2,4,5,10,20

Factors of 75

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

1,3,5,15,25,75

Greatest Common Factor

We found the factors 86,84,20,75 . The biggest common factor number is the GCF number.
So the greatest common factor 86,84,20,75 is 1.

Lets's calculate LCM of 13,54,24,342

2 13, 54, 24, 342
3 13, 27, 12, 171
3 13, 9, 4, 57
13, 3, 4, 19

∴ So the LCM of the given numbers is 2 x 3 x 3 x 13 x 3 x 4 x 19 = 53352

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/53352

Therefore, the GCF of Fractions 86/13,84/54,20/24,75/342 is 1/53352

Least Common Multiple of 13,54,24,342 with GCF Formula

Least Common Multiple of 13,54,24,342 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 13,54,24,342 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(13,54,24,342) = 1

common factors(in case of two or more numbers have common factors) = 108

GCF(13,54,24,342) x common factors =1 x 108 = 108

LCM(13,54,24,342) = ( 13 × 54 × 24 × 342 ) / 108

LCM(13,54,24,342) = 5762016 / 108

LCM(13,54,24,342) = 53352


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 86/13, 84/54, 20/24, 75/342

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 86/13, 84/54, 20/24, 75/342?

Answer: GCF of Numerators as per given numbers 86/13, 84/54, 20/24, 75/342 is

GCF of Numerators i.e. for 86,84,20,75 is 1

LCM of denominators i.e. for 13,54,24,342 is 53352.

Thus, GCF of Fractions is 1/53352.Finally, GCF of Fractions for 86/13, 84/54, 20/24, 75/342 is 1/53352.