Greatest Common Factor of 82/420, 194/306

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

GCF of 82/420, 194/306

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 82/420,194/306

Given fractions are 82/420,194/306

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 82,194

Greatest Common Factor of Numerators i.e. GCF of 82,194 is 2 .

LCM of Denominators means LCM of 420,306 as per the given fractions.

LCM of 420,306 is 21420 as it is the smallest common factor for both these numbers.

Lets's calculate GCF of 82,194

GCF of Fractions 82/420,194/306 is 2/21420

2 82, 194
41, 97

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

Greatest Common Factor of 82,194 By Matching Biggest Common Factor Method

Greatest Common Factor of 82,194 By Matching Biggest Common Factor Method

Factors of 82

List of positive integer factors of 82 that divides 82 without a remainder.

1,2,41,82

Factors of 194

List of positive integer factors of 194 that divides 194 without a remainder.

1,2,97,194

Greatest Common Factor

We found the factors 82,194 . The biggest common factor number is the GCF number.
So the greatest common factor 82,194 is 2.

Lets's calculate LCM of 420,306

2 420, 306
3 210, 153
70, 51

∴ So the LCM of the given numbers is 2 x 3 x 70 x 51 = 21420

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/21420

Therefore, the GCF of Fractions 82/420,194/306 is 2/21420

Least Common Multiple of 420,306 with GCF Formula

Least Common Multiple of 420,306 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 420,306 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(420,306) = 6

common factors(in case of two or more numbers have common factors) = 1

GCF(420,306) x common factors =6 x 1 = 6

LCM(420,306) = ( 420 × 306 ) / 6

LCM(420,306) = 128520 / 6

LCM(420,306) = 21420


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 82/420, 194/306

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 82/420, 194/306?

Answer: GCF of Numerators as per given numbers 82/420, 194/306 is

GCF of Numerators i.e. for 82,194 is 2

LCM of denominators i.e. for 420,306 is 21420.

Thus, GCF of Fractions is 2/21420.Finally, GCF of Fractions for 82/420, 194/306 is 2/21420.