Greatest Common Factor of 14/22, 20/64, 74/78, 75/321

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

GCF of 14/22, 20/64, 74/78, 75/321

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 14/22,20/64,74/78,75/321

Given fractions are 14/22,20/64,74/78,75/321

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 14,20,74,75

Greatest Common Factor of Numerators i.e. GCF of 14,20,74,75 is 1 .

LCM of Denominators means LCM of 22,64,78,321 as per the given fractions.

LCM of 22,64,78,321 is 2937792 as it is the smallest common factor for both these numbers.

Lets's calculate GCF of 14,20,74,75

GCF of Fractions 14/22,20/64,74/78,75/321 is 1/2937792

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

Greatest Common Factor of 14,20,74,75 By Matching Biggest Common Factor Method

Greatest Common Factor of 14,20,74,75 By Matching Biggest Common Factor Method

Factors of 14

List of positive integer factors of 14 that divides 14 without a remainder.

1,2,7,14

Factors of 20

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

1,2,4,5,10,20

Factors of 74

List of positive integer factors of 74 that divides 74 without a remainder.

1,2,37,74

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 14,20,74,75 . The biggest common factor number is the GCF number.
So the greatest common factor 14,20,74,75 is 1.

Lets's calculate LCM of 22,64,78,321

2 22, 64, 78, 321
3 11, 32, 39, 321
11, 32, 13, 107

∴ So the LCM of the given numbers is 2 x 3 x 11 x 32 x 13 x 107 = 2937792

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/2937792

Therefore, the GCF of Fractions 14/22,20/64,74/78,75/321 is 1/2937792

Least Common Multiple of 22,64,78,321 with GCF Formula

Least Common Multiple of 22,64,78,321 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 22,64,78,321 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(22,64,78,321) = 1

common factors(in case of two or more numbers have common factors) = 12

GCF(22,64,78,321) x common factors =1 x 12 = 12

LCM(22,64,78,321) = ( 22 × 64 × 78 × 321 ) / 12

LCM(22,64,78,321) = 35253504 / 12

LCM(22,64,78,321) = 2937792


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 14/22, 20/64, 74/78, 75/321

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 14/22, 20/64, 74/78, 75/321?

Answer: GCF of Numerators as per given numbers 14/22, 20/64, 74/78, 75/321 is

GCF of Numerators i.e. for 14,20,74,75 is 1

LCM of denominators i.e. for 22,64,78,321 is 2937792.

Thus, GCF of Fractions is 1/2937792.Finally, GCF of Fractions for 14/22, 20/64, 74/78, 75/321 is 1/2937792.