Greatest Common Factor of 74/34, 20/14, 76/30, 98/312

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

GCF of 74/34, 20/14, 76/30, 98/312

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 74/34,20/14,76/30,98/312

Given fractions are 74/34,20/14,76/30,98/312

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 74,20,76,98

Greatest Common Factor of Numerators i.e. GCF of 74,20,76,98 is 2 .

LCM of Denominators means LCM of 34,14,30,312 as per the given fractions.

LCM of 34,14,30,312 is 185640 as it is the smallest common factor for both these numbers.

Lets's calculate GCF of 74,20,76,98

GCF of Fractions 74/34,20/14,76/30,98/312 is 2/185640

2 74, 20, 76, 98
37, 10, 38, 49

∴ So the GCF of the given numbers is 2 = 2

Greatest Common Factor of 74,20,76,98 By Matching Biggest Common Factor Method

Greatest Common Factor of 74,20,76,98 By Matching Biggest Common Factor Method

Factors of 74

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

1,2,37,74

Factors of 20

List of positive integer factors of 20 that divides 20 without a remainder.

1,2,4,5,10,20

Factors of 76

List of positive integer factors of 76 that divides 76 without a remainder.

1,2,4,19,38,76

Factors of 98

List of positive integer factors of 98 that divides 98 without a remainder.

1,2,7,14,49,98

Greatest Common Factor

We found the factors 74,20,76,98 . The biggest common factor number is the GCF number.
So the greatest common factor 74,20,76,98 is 2.

Lets's calculate LCM of 34,14,30,312

2 34, 14, 30, 312
3 17, 7, 15, 156
17, 7, 5, 52

∴ So the LCM of the given numbers is 2 x 3 x 17 x 7 x 5 x 52 = 185640

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/185640

Therefore, the GCF of Fractions 74/34,20/14,76/30,98/312 is 2/185640

Least Common Multiple of 34,14,30,312 with GCF Formula

Least Common Multiple of 34,14,30,312 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 34,14,30,312 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(34,14,30,312) = 2

common factors(in case of two or more numbers have common factors) = 12

GCF(34,14,30,312) x common factors =2 x 12 = 24

LCM(34,14,30,312) = ( 34 × 14 × 30 × 312 ) / 24

LCM(34,14,30,312) = 4455360 / 24

LCM(34,14,30,312) = 185640


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 74/34, 20/14, 76/30, 98/312

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 74/34, 20/14, 76/30, 98/312?

Answer: GCF of Numerators as per given numbers 74/34, 20/14, 76/30, 98/312 is

GCF of Numerators i.e. for 74,20,76,98 is 2

LCM of denominators i.e. for 34,14,30,312 is 185640.

Thus, GCF of Fractions is 2/185640.Finally, GCF of Fractions for 74/34, 20/14, 76/30, 98/312 is 2/185640.