Greatest Common Factor of 138/75, 412/410

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

GCF of 138/75, 412/410

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 138/75,412/410

Given fractions are 138/75,412/410

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 138,412

Greatest Common Factor of Numerators i.e. GCF of 138,412 is 2 .

LCM of Denominators means LCM of 75,410 as per the given fractions.

LCM of 75,410 is 6150 as it is the smallest common factor for both these numbers.

Lets's calculate GCF of 138,412

GCF of Fractions 138/75,412/410 is 2/6150

2 138, 412
69, 206

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

Greatest Common Factor of 138,412 By Matching Biggest Common Factor Method

Greatest Common Factor of 138,412 By Matching Biggest Common Factor Method

Factors of 138

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

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

Factors of 412

List of positive integer factors of 412 that divides 412 without a remainder.

1,2,4,103,206,412

Greatest Common Factor

We found the factors 138,412 . The biggest common factor number is the GCF number.
So the greatest common factor 138,412 is 2.

Lets's calculate LCM of 75,410

5 75, 410
15, 82

∴ So the LCM of the given numbers is 5 x 15 x 82 = 6150

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/6150

Therefore, the GCF of Fractions 138/75,412/410 is 2/6150

Least Common Multiple of 75,410 with GCF Formula

Least Common Multiple of 75,410 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 75,410 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(75,410) = 5

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

GCF(75,410) x common factors =5 x 1 = 5

LCM(75,410) = ( 75 × 410 ) / 5

LCM(75,410) = 30750 / 5

LCM(75,410) = 6150


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 138/75, 412/410

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 138/75, 412/410?

Answer: GCF of Numerators as per given numbers 138/75, 412/410 is

GCF of Numerators i.e. for 138,412 is 2

LCM of denominators i.e. for 75,410 is 6150.

Thus, GCF of Fractions is 2/6150.Finally, GCF of Fractions for 138/75, 412/410 is 2/6150.