Greatest Common Factor of 27/21, 89/60, 31/55, 10/210

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

GCF of 27/21, 89/60, 31/55, 10/210

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 27/21,89/60,31/55,10/210

Given fractions are 27/21,89/60,31/55,10/210

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 27,89,31,10

Greatest Common Factor of Numerators i.e. GCF of 27,89,31,10 is 1 .

LCM of Denominators means LCM of 21,60,55,210 as per the given fractions.

LCM of 21,60,55,210 is 4620 as it is the smallest common factor for both these numbers.

Lets's calculate GCF of 27,89,31,10

GCF of Fractions 27/21,89/60,31/55,10/210 is 1/4620

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

Greatest Common Factor of 27,89,31,10 By Matching Biggest Common Factor Method

Greatest Common Factor of 27,89,31,10 By Matching Biggest Common Factor Method

Factors of 27

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

1,3,9,27

Factors of 89

List of positive integer factors of 89 that divides 89 without a remainder.

1,89

Factors of 31

List of positive integer factors of 31 that divides 31 without a remainder.

1,31

Factors of 10

List of positive integer factors of 10 that divides 10 without a remainder.

1,2,5,10

Greatest Common Factor

We found the factors 27,89,31,10 . The biggest common factor number is the GCF number.
So the greatest common factor 27,89,31,10 is 1.

Lets's calculate LCM of 21,60,55,210

2 21, 60, 55, 210
3 21, 30, 55, 105
5 7, 10, 55, 35
7 7, 2, 11, 7
1, 2, 11, 1

∴ So the LCM of the given numbers is 2 x 3 x 5 x 7 x 1 x 2 x 11 x 1 = 4620

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/4620

Therefore, the GCF of Fractions 27/21,89/60,31/55,10/210 is 1/4620

Least Common Multiple of 21,60,55,210 with GCF Formula

Least Common Multiple of 21,60,55,210 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 21,60,55,210 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(21,60,55,210) = 1

common factors(in case of two or more numbers have common factors) = 3150

GCF(21,60,55,210) x common factors =1 x 3150 = 3150

LCM(21,60,55,210) = ( 21 × 60 × 55 × 210 ) / 3150

LCM(21,60,55,210) = 14553000 / 3150

LCM(21,60,55,210) = 4620


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 27/21, 89/60, 31/55, 10/210

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 27/21, 89/60, 31/55, 10/210?

Answer: GCF of Numerators as per given numbers 27/21, 89/60, 31/55, 10/210 is

GCF of Numerators i.e. for 27,89,31,10 is 1

LCM of denominators i.e. for 21,60,55,210 is 4620.

Thus, GCF of Fractions is 1/4620.Finally, GCF of Fractions for 27/21, 89/60, 31/55, 10/210 is 1/4620.