Greatest Common Factor of 78/275, 135/414

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

GCF of 78/275, 135/414

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 78/275,135/414

Given fractions are 78/275,135/414

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 78,135

Greatest Common Factor of Numerators i.e. GCF of 78,135 is 3 .

LCM of Denominators means LCM of 275,414 as per the given fractions.

LCM of 275,414 is 113850 as it is the smallest common factor for both these numbers.

Lets's calculate GCF of 78,135

GCF of Fractions 78/275,135/414 is 3/113850

3 78, 135
26, 45

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

Greatest Common Factor of 78,135 By Matching Biggest Common Factor Method

Greatest Common Factor of 78,135 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 135

List of positive integer factors of 135 that divides 135 without a remainder.

1,3,5,9,15,27,45,135

Greatest Common Factor

We found the factors 78,135 . The biggest common factor number is the GCF number.
So the greatest common factor 78,135 is 3.

Lets's calculate LCM of 275,414

Given numbers has no common factors except 1. So, there LCM is their product i.e 113850

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 3/113850

Therefore, the GCF of Fractions 78/275,135/414 is 3/113850

Least Common Multiple of 275,414 with GCF Formula

Least Common Multiple of 275,414 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 275,414 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(275,414) = 1

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

GCF(275,414) x common factors =1 x 1 = 1

LCM(275,414) = ( 275 × 414 ) / 1

LCM(275,414) = 113850 / 1

LCM(275,414) = 113850


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 78/275, 135/414

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 78/275, 135/414?

Answer: GCF of Numerators as per given numbers 78/275, 135/414 is

GCF of Numerators i.e. for 78,135 is 3

LCM of denominators i.e. for 275,414 is 113850.

Thus, GCF of Fractions is 3/113850.Finally, GCF of Fractions for 78/275, 135/414 is 3/113850.