Greatest Common Factor of 14/27, 59/75, 21/40, 49/18

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

GCF of 14/27, 59/75, 21/40, 49/18

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 14/27,59/75,21/40,49/18

Given fractions are 14/27,59/75,21/40,49/18

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 14,59,21,49

Greatest Common Factor of Numerators i.e. GCF of 14,59,21,49 is 1 .

LCM of Denominators means LCM of 27,75,40,18 as per the given fractions.

LCM of 27,75,40,18 is 5400 as it is the smallest common factor for both these numbers.

Lets's calculate GCF of 14,59,21,49

GCF of Fractions 14/27,59/75,21/40,49/18 is 1/5400

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

Greatest Common Factor of 14,59,21,49 By Matching Biggest Common Factor Method

Greatest Common Factor of 14,59,21,49 By Matching Biggest Common Factor Method

Factors of 14

List of positive integer factors of 14 that divides 14 without a remainder.

1,2,7,14

Factors of 59

List of positive integer factors of 59 that divides 59 without a remainder.

1,59

Factors of 21

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

1,3,7,21

Factors of 49

List of positive integer factors of 49 that divides 49 without a remainder.

1,7,49

Greatest Common Factor

We found the factors 14,59,21,49 . The biggest common factor number is the GCF number.
So the greatest common factor 14,59,21,49 is 1.

Lets's calculate LCM of 27,75,40,18

2 27, 75, 40, 18
3 27, 75, 20, 9
3 3, 25, 20, 9
5 1, 25, 20, 3
1, 5, 4, 3

∴ So the LCM of the given numbers is 2 x 3 x 3 x 5 x 1 x 5 x 4 x 3 = 5400

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/5400

Therefore, the GCF of Fractions 14/27,59/75,21/40,49/18 is 1/5400

Least Common Multiple of 27,75,40,18 with GCF Formula

Least Common Multiple of 27,75,40,18 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 27,75,40,18 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(27,75,40,18) = 1

common factors(in case of two or more numbers have common factors) = 270

GCF(27,75,40,18) x common factors =1 x 270 = 270

LCM(27,75,40,18) = ( 27 × 75 × 40 × 18 ) / 270

LCM(27,75,40,18) = 1458000 / 270

LCM(27,75,40,18) = 5400


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 14/27, 59/75, 21/40, 49/18

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 14/27, 59/75, 21/40, 49/18?

Answer: GCF of Numerators as per given numbers 14/27, 59/75, 21/40, 49/18 is

GCF of Numerators i.e. for 14,59,21,49 is 1

LCM of denominators i.e. for 27,75,40,18 is 5400.

Thus, GCF of Fractions is 1/5400.Finally, GCF of Fractions for 14/27, 59/75, 21/40, 49/18 is 1/5400.