Greatest Common Factor of 36/75, 76/51, 820/21

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

GCF of 36/75, 76/51, 820/21

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 36/75,76/51,820/21

Given fractions are 36/75,76/51,820/21

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 36,76,820

Greatest Common Factor of Numerators i.e. GCF of 36,76,820 is 4 .

LCM of Denominators means LCM of 75,51,21 as per the given fractions.

LCM of 75,51,21 is 8925 as it is the smallest common factor for both these numbers.

Lets's calculate GCF of 36,76,820

GCF of Fractions 36/75,76/51,820/21 is 4/8925

2 36, 76, 820
2 18, 38, 410
9, 19, 205

∴ So the GCF of the given numbers is 2 x 2 = 4

Greatest Common Factor of 36,76,820 By Matching Biggest Common Factor Method

Greatest Common Factor of 36,76,820 By Matching Biggest Common Factor Method

Factors of 36

List of positive integer factors of 36 that divides 36 without a remainder.

1,2,3,4,6,9,12,18,36

Factors of 76

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

1,2,4,19,38,76

Factors of 820

List of positive integer factors of 820 that divides 820 without a remainder.

1,2,4,5,10,20,41,82,164,205,410,820

Greatest Common Factor

We found the factors 36,76,820 . The biggest common factor number is the GCF number.
So the greatest common factor 36,76,820 is 4.

Lets's calculate LCM of 75,51,21

3 75, 51, 21
25, 17, 7

∴ So the LCM of the given numbers is 3 x 25 x 17 x 7 = 8925

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 4/8925

Therefore, the GCF of Fractions 36/75,76/51,820/21 is 4/8925

Least Common Multiple of 75,51,21 with GCF Formula

Least Common Multiple of 75,51,21 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 75,51,21 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(75,51,21) = 3

common factors(in case of two or more numbers have common factors) = 3

GCF(75,51,21) x common factors =3 x 3 = 9

LCM(75,51,21) = ( 75 × 51 × 21 ) / 9

LCM(75,51,21) = 80325 / 9

LCM(75,51,21) = 8925


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 36/75, 76/51, 820/21

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 36/75, 76/51, 820/21?

Answer: GCF of Numerators as per given numbers 36/75, 76/51, 820/21 is

GCF of Numerators i.e. for 36,76,820 is 4

LCM of denominators i.e. for 75,51,21 is 8925.

Thus, GCF of Fractions is 4/8925.Finally, GCF of Fractions for 36/75, 76/51, 820/21 is 4/8925.