Greatest Common Factor of 13/84, 45/64, 76/38, 20/96

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

GCF of 13/84, 45/64, 76/38, 20/96

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 13/84,45/64,76/38,20/96

Given fractions are 13/84,45/64,76/38,20/96

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 13,45,76,20

Greatest Common Factor of Numerators i.e. GCF of 13,45,76,20 is 1 .

LCM of Denominators means LCM of 84,64,38,96 as per the given fractions.

LCM of 84,64,38,96 is 25536 as it is the smallest common factor for both these numbers.

Lets's calculate GCF of 13,45,76,20

GCF of Fractions 13/84,45/64,76/38,20/96 is 1/25536

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

Greatest Common Factor of 13,45,76,20 By Matching Biggest Common Factor Method

Greatest Common Factor of 13,45,76,20 By Matching Biggest Common Factor Method

Factors of 13

List of positive integer factors of 13 that divides 13 without a remainder.

1,13

Factors of 45

List of positive integer factors of 45 that divides 45 without a remainder.

1,3,5,9,15,45

Factors of 76

List of positive integer factors of 76 that divides 76 without a remainder.

1,2,4,19,38,76

Factors of 20

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

1,2,4,5,10,20

Greatest Common Factor

We found the factors 13,45,76,20 . The biggest common factor number is the GCF number.
So the greatest common factor 13,45,76,20 is 1.

Lets's calculate LCM of 84,64,38,96

2 84, 64, 38, 96
2 42, 32, 19, 48
2 21, 16, 19, 24
2 21, 8, 19, 12
2 21, 4, 19, 6
3 21, 2, 19, 3
7, 2, 19, 1

∴ So the LCM of the given numbers is 2 x 2 x 2 x 2 x 2 x 3 x 7 x 2 x 19 x 1 = 25536

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/25536

Therefore, the GCF of Fractions 13/84,45/64,76/38,20/96 is 1/25536

Least Common Multiple of 84,64,38,96 with GCF Formula

Least Common Multiple of 84,64,38,96 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 84,64,38,96 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(84,64,38,96) = 2

common factors(in case of two or more numbers have common factors) = 384

GCF(84,64,38,96) x common factors =2 x 384 = 768

LCM(84,64,38,96) = ( 84 × 64 × 38 × 96 ) / 768

LCM(84,64,38,96) = 19611648 / 768

LCM(84,64,38,96) = 25536


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 13/84, 45/64, 76/38, 20/96

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 13/84, 45/64, 76/38, 20/96?

Answer: GCF of Numerators as per given numbers 13/84, 45/64, 76/38, 20/96 is

GCF of Numerators i.e. for 13,45,76,20 is 1

LCM of denominators i.e. for 84,64,38,96 is 25536.

Thus, GCF of Fractions is 1/25536.Finally, GCF of Fractions for 13/84, 45/64, 76/38, 20/96 is 1/25536.