Greatest Common Factor of 87/39, 60/30, 21/82, 69/22

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

GCF of 87/39, 60/30, 21/82, 69/22

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 87/39,60/30,21/82,69/22

Given fractions are 87/39,60/30,21/82,69/22

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 87,60,21,69

Greatest Common Factor of Numerators i.e. GCF of 87,60,21,69 is 3 .

LCM of Denominators means LCM of 39,30,82,22 as per the given fractions.

LCM of 39,30,82,22 is 175890 as it is the smallest common factor for both these numbers.

Lets's calculate GCF of 87,60,21,69

GCF of Fractions 87/39,60/30,21/82,69/22 is 3/175890

3 87, 60, 21, 69
29, 20, 7, 23

∴ So the GCF of the given numbers is 3 = 3

Greatest Common Factor of 87,60,21,69 By Matching Biggest Common Factor Method

Greatest Common Factor of 87,60,21,69 By Matching Biggest Common Factor Method

Factors of 87

List of positive integer factors of 87 that divides 87 without a remainder.

1,3,29,87

Factors of 60

List of positive integer factors of 60 that divides 60 without a remainder.

1,2,3,4,5,6,10,12,15,20,30,60

Factors of 21

List of positive integer factors of 21 that divides 21 without a remainder.

1,3,7,21

Factors of 69

List of positive integer factors of 69 that divides 69 without a remainder.

1,3,23,69

Greatest Common Factor

We found the factors 87,60,21,69 . The biggest common factor number is the GCF number.
So the greatest common factor 87,60,21,69 is 3.

Lets's calculate LCM of 39,30,82,22

2 39, 30, 82, 22
3 39, 15, 41, 11
13, 5, 41, 11

∴ So the LCM of the given numbers is 2 x 3 x 13 x 5 x 41 x 11 = 175890

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 3/175890

Therefore, the GCF of Fractions 87/39,60/30,21/82,69/22 is 3/175890

Least Common Multiple of 39,30,82,22 with GCF Formula

Least Common Multiple of 39,30,82,22 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 39,30,82,22 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(39,30,82,22) = 1

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

GCF(39,30,82,22) x common factors =1 x 12 = 12

LCM(39,30,82,22) = ( 39 × 30 × 82 × 22 ) / 12

LCM(39,30,82,22) = 2110680 / 12

LCM(39,30,82,22) = 175890


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 87/39, 60/30, 21/82, 69/22

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 87/39, 60/30, 21/82, 69/22?

Answer: GCF of Numerators as per given numbers 87/39, 60/30, 21/82, 69/22 is

GCF of Numerators i.e. for 87,60,21,69 is 3

LCM of denominators i.e. for 39,30,82,22 is 175890.

Thus, GCF of Fractions is 3/175890.Finally, GCF of Fractions for 87/39, 60/30, 21/82, 69/22 is 3/175890.