Greatest Common Factor of 6/63, 21/81, 27/108, 105/120

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

GCF of 6/63, 21/81, 27/108, 105/120

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 6/63,21/81,27/108,105/120

Given fractions are 6/63,21/81,27/108,105/120

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 6,21,27,105

Greatest Common Factor of Numerators i.e. GCF of 6,21,27,105 is 3 .

LCM of Denominators means LCM of 63,81,108,120 as per the given fractions.

LCM of 63,81,108,120 is 22680 as it is the smallest common factor for both these numbers.

Lets's calculate GCF of 6,21,27,105

GCF of Fractions 6/63,21/81,27/108,105/120 is 3/22680

3 6, 21, 27, 105
2, 7, 9, 35

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

Greatest Common Factor of 6,21,27,105 By Matching Biggest Common Factor Method

Greatest Common Factor of 6,21,27,105 By Matching Biggest Common Factor Method

Factors of 6

List of positive integer factors of 6 that divides 6 without a remainder.

1,2,3,6

Factors of 21

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

1,3,7,21

Factors of 27

List of positive integer factors of 27 that divides 27 without a remainder.

1,3,9,27

Factors of 105

List of positive integer factors of 105 that divides 105 without a remainder.

1,3,5,7,15,21,35,105

Greatest Common Factor

We found the factors 6,21,27,105 . The biggest common factor number is the GCF number.
So the greatest common factor 6,21,27,105 is 3.

Lets's calculate LCM of 63,81,108,120

2 63, 81, 108, 120
2 63, 81, 54, 60
3 63, 81, 27, 30
3 21, 9, 27, 10
3 7, 3, 9, 10
7, 1, 3, 10

∴ So the LCM of the given numbers is 2 x 2 x 3 x 3 x 3 x 7 x 1 x 3 x 10 = 22680

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 3/22680

Therefore, the GCF of Fractions 6/63,21/81,27/108,105/120 is 3/22680

Least Common Multiple of 63,81,108,120 with GCF Formula

Least Common Multiple of 63,81,108,120 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 63,81,108,120 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(63,81,108,120) = 3

common factors(in case of two or more numbers have common factors) = 972

GCF(63,81,108,120) x common factors =3 x 972 = 2916

LCM(63,81,108,120) = ( 63 × 81 × 108 × 120 ) / 2916

LCM(63,81,108,120) = 66134880 / 2916

LCM(63,81,108,120) = 22680


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 6/63, 21/81, 27/108, 105/120

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 6/63, 21/81, 27/108, 105/120?

Answer: GCF of Numerators as per given numbers 6/63, 21/81, 27/108, 105/120 is

GCF of Numerators i.e. for 6,21,27,105 is 3

LCM of denominators i.e. for 63,81,108,120 is 22680.

Thus, GCF of Fractions is 3/22680.Finally, GCF of Fractions for 6/63, 21/81, 27/108, 105/120 is 3/22680.