Greatest Common Factor of 21/77, 69/30, 66/72, 75/10

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

GCF of 21/77, 69/30, 66/72, 75/10

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 21/77,69/30,66/72,75/10

Given fractions are 21/77,69/30,66/72,75/10

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 21,69,66,75

Greatest Common Factor of Numerators i.e. GCF of 21,69,66,75 is 3 .

LCM of Denominators means LCM of 77,30,72,10 as per the given fractions.

LCM of 77,30,72,10 is 27720 as it is the smallest common factor for both these numbers.

Lets's calculate GCF of 21,69,66,75

GCF of Fractions 21/77,69/30,66/72,75/10 is 3/27720

3 21, 69, 66, 75
7, 23, 22, 25

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

Greatest Common Factor of 21,69,66,75 By Matching Biggest Common Factor Method

Greatest Common Factor of 21,69,66,75 By Matching Biggest Common Factor Method

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

Factors of 66

List of positive integer factors of 66 that divides 66 without a remainder.

1,2,3,6,11,22,33,66

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 21,69,66,75 . The biggest common factor number is the GCF number.
So the greatest common factor 21,69,66,75 is 3.

Lets's calculate LCM of 77,30,72,10

2 77, 30, 72, 10
3 77, 15, 36, 5
5 77, 5, 12, 5
77, 1, 12, 1

∴ So the LCM of the given numbers is 2 x 3 x 5 x 77 x 1 x 12 x 1 = 27720

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 3/27720

Therefore, the GCF of Fractions 21/77,69/30,66/72,75/10 is 3/27720

Least Common Multiple of 77,30,72,10 with GCF Formula

Least Common Multiple of 77,30,72,10 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 77,30,72,10 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(77,30,72,10) = 1

common factors(in case of two or more numbers have common factors) = 60

GCF(77,30,72,10) x common factors =1 x 60 = 60

LCM(77,30,72,10) = ( 77 × 30 × 72 × 10 ) / 60

LCM(77,30,72,10) = 1663200 / 60

LCM(77,30,72,10) = 27720


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 21/77, 69/30, 66/72, 75/10

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 21/77, 69/30, 66/72, 75/10?

Answer: GCF of Numerators as per given numbers 21/77, 69/30, 66/72, 75/10 is

GCF of Numerators i.e. for 21,69,66,75 is 3

LCM of denominators i.e. for 77,30,72,10 is 27720.

Thus, GCF of Fractions is 3/27720.Finally, GCF of Fractions for 21/77, 69/30, 66/72, 75/10 is 3/27720.