Greatest Common Factor of 42/98, 81/21, 91/36, 109/32

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

GCF of 42/98, 81/21, 91/36, 109/32

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 42/98,81/21,91/36,109/32

Given fractions are 42/98,81/21,91/36,109/32

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 42,81,91,109

Greatest Common Factor of Numerators i.e. GCF of 42,81,91,109 is 1 .

LCM of Denominators means LCM of 98,21,36,32 as per the given fractions.

LCM of 98,21,36,32 is 14112 as it is the smallest common factor for both these numbers.

Lets's calculate GCF of 42,81,91,109

GCF of Fractions 42/98,81/21,91/36,109/32 is 1/14112

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

Greatest Common Factor of 42,81,91,109 By Matching Biggest Common Factor Method

Greatest Common Factor of 42,81,91,109 By Matching Biggest Common Factor Method

Factors of 42

List of positive integer factors of 42 that divides 42 without a remainder.

1,2,3,6,7,14,21,42

Factors of 81

List of positive integer factors of 81 that divides 81 without a remainder.

1,3,9,27,81

Factors of 91

List of positive integer factors of 91 that divides 91 without a remainder.

1,7,13,91

Factors of 109

List of positive integer factors of 109 that divides 109 without a remainder.

1,109

Greatest Common Factor

We found the factors 42,81,91,109 . The biggest common factor number is the GCF number.
So the greatest common factor 42,81,91,109 is 1.

Lets's calculate LCM of 98,21,36,32

2 98, 21, 36, 32
2 49, 21, 18, 16
3 49, 21, 9, 8
7 49, 7, 3, 8
1, 7, 3, 8

∴ So the LCM of the given numbers is 2 x 2 x 3 x 7 x 1 x 7 x 3 x 8 = 14112

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/14112

Therefore, the GCF of Fractions 42/98,81/21,91/36,109/32 is 1/14112

Least Common Multiple of 98,21,36,32 with GCF Formula

Least Common Multiple of 98,21,36,32 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 98,21,36,32 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(98,21,36,32) = 1

common factors(in case of two or more numbers have common factors) = 168

GCF(98,21,36,32) x common factors =1 x 168 = 168

LCM(98,21,36,32) = ( 98 × 21 × 36 × 32 ) / 168

LCM(98,21,36,32) = 2370816 / 168

LCM(98,21,36,32) = 14112


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 42/98, 81/21, 91/36, 109/32

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 42/98, 81/21, 91/36, 109/32?

Answer: GCF of Numerators as per given numbers 42/98, 81/21, 91/36, 109/32 is

GCF of Numerators i.e. for 42,81,91,109 is 1

LCM of denominators i.e. for 98,21,36,32 is 14112.

Thus, GCF of Fractions is 1/14112.Finally, GCF of Fractions for 42/98, 81/21, 91/36, 109/32 is 1/14112.