Greatest Common Factor of 27/98, 74/38, 17/14, 219/90

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

GCF of 27/98, 74/38, 17/14, 219/90

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 27/98,74/38,17/14,219/90

Given fractions are 27/98,74/38,17/14,219/90

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 27,74,17,219

Greatest Common Factor of Numerators i.e. GCF of 27,74,17,219 is 1 .

LCM of Denominators means LCM of 98,38,14,90 as per the given fractions.

LCM of 98,38,14,90 is 83790 as it is the smallest common factor for both these numbers.

Lets's calculate GCF of 27,74,17,219

GCF of Fractions 27/98,74/38,17/14,219/90 is 1/83790

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

Greatest Common Factor of 27,74,17,219 By Matching Biggest Common Factor Method

Greatest Common Factor of 27,74,17,219 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 74

List of positive integer factors of 74 that divides 74 without a remainder.

1,2,37,74

Factors of 17

List of positive integer factors of 17 that divides 17 without a remainder.

1,17

Factors of 219

List of positive integer factors of 219 that divides 219 without a remainder.

1,3,73,219

Greatest Common Factor

We found the factors 27,74,17,219 . The biggest common factor number is the GCF number.
So the greatest common factor 27,74,17,219 is 1.

Lets's calculate LCM of 98,38,14,90

2 98, 38, 14, 90
7 49, 19, 7, 45
1, 19, 7, 45

∴ So the LCM of the given numbers is 2 x 7 x 1 x 19 x 7 x 45 = 83790

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/83790

Therefore, the GCF of Fractions 27/98,74/38,17/14,219/90 is 1/83790

Least Common Multiple of 98,38,14,90 with GCF Formula

Least Common Multiple of 98,38,14,90 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 98,38,14,90 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(98,38,14,90) = 2

common factors(in case of two or more numbers have common factors) = 28

GCF(98,38,14,90) x common factors =2 x 28 = 56

LCM(98,38,14,90) = ( 98 × 38 × 14 × 90 ) / 56

LCM(98,38,14,90) = 4692240 / 56

LCM(98,38,14,90) = 83790


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 27/98, 74/38, 17/14, 219/90

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 27/98, 74/38, 17/14, 219/90?

Answer: GCF of Numerators as per given numbers 27/98, 74/38, 17/14, 219/90 is

GCF of Numerators i.e. for 27,74,17,219 is 1

LCM of denominators i.e. for 98,38,14,90 is 83790.

Thus, GCF of Fractions is 1/83790.Finally, GCF of Fractions for 27/98, 74/38, 17/14, 219/90 is 1/83790.