Greatest Common Factor of 78/322, 249/233, 138/105

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

GCF of 78/322, 249/233, 138/105

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 78/322,249/233,138/105

Given fractions are 78/322,249/233,138/105

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 78,249,138

Greatest Common Factor of Numerators i.e. GCF of 78,249,138 is 3 .

LCM of Denominators means LCM of 322,233,105 as per the given fractions.

LCM of 322,233,105 is 1125390 as it is the smallest common factor for both these numbers.

Lets's calculate GCF of 78,249,138

GCF of Fractions 78/322,249/233,138/105 is 3/1125390

3 78, 249, 138
26, 83, 46

∴ So the GCF of the given numbers is 3 = 3

Greatest Common Factor of 78,249,138 By Matching Biggest Common Factor Method

Greatest Common Factor of 78,249,138 By Matching Biggest Common Factor Method

Factors of 78

List of positive integer factors of 78 that divides 78 without a remainder.

1,2,3,6,13,26,39,78

Factors of 249

List of positive integer factors of 249 that divides 249 without a remainder.

1,3,83,249

Factors of 138

List of positive integer factors of 138 that divides 138 without a remainder.

1,2,3,6,23,46,69,138

Greatest Common Factor

We found the factors 78,249,138 . The biggest common factor number is the GCF number.
So the greatest common factor 78,249,138 is 3.

Lets's calculate LCM of 322,233,105

7 322, 233, 105
46, 233, 15

∴ So the LCM of the given numbers is 7 x 46 x 233 x 15 = 1125390

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 3/1125390

Therefore, the GCF of Fractions 78/322,249/233,138/105 is 3/1125390

Least Common Multiple of 322,233,105 with GCF Formula

Least Common Multiple of 322,233,105 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 322,233,105 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(322,233,105) = 1

common factors(in case of two or more numbers have common factors) = 7

GCF(322,233,105) x common factors =1 x 7 = 7

LCM(322,233,105) = ( 322 × 233 × 105 ) / 7

LCM(322,233,105) = 7877730 / 7

LCM(322,233,105) = 1125390


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 78/322, 249/233, 138/105

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 78/322, 249/233, 138/105?

Answer: GCF of Numerators as per given numbers 78/322, 249/233, 138/105 is

GCF of Numerators i.e. for 78,249,138 is 3

LCM of denominators i.e. for 322,233,105 is 1125390.

Thus, GCF of Fractions is 3/1125390.Finally, GCF of Fractions for 78/322, 249/233, 138/105 is 3/1125390.