Greatest Common Factor of 106/75, 409/77, 559/415

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

GCF of 106/75, 409/77, 559/415

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 106/75,409/77,559/415

Given fractions are 106/75,409/77,559/415

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 106,409,559

Greatest Common Factor of Numerators i.e. GCF of 106,409,559 is 1 .

LCM of Denominators means LCM of 75,77,415 as per the given fractions.

LCM of 75,77,415 is 479325 as it is the smallest common factor for both these numbers.

Lets's calculate GCF of 106,409,559

GCF of Fractions 106/75,409/77,559/415 is 1/479325

∴ So GCF of numbers is 1 because of no common factors present between them.

Greatest Common Factor of 106,409,559 By Matching Biggest Common Factor Method

Greatest Common Factor of 106,409,559 By Matching Biggest Common Factor Method

Factors of 106

List of positive integer factors of 106 that divides 106 without a remainder.

1,2,53,106

Factors of 409

List of positive integer factors of 409 that divides 409 without a remainder.

1,409

Factors of 559

List of positive integer factors of 559 that divides 559 without a remainder.

1,13,43,559

Greatest Common Factor

We found the factors 106,409,559 . The biggest common factor number is the GCF number.
So the greatest common factor 106,409,559 is 1.

Lets's calculate LCM of 75,77,415

5 75, 77, 415
15, 77, 83

∴ So the LCM of the given numbers is 5 x 15 x 77 x 83 = 479325

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/479325

Therefore, the GCF of Fractions 106/75,409/77,559/415 is 1/479325

Least Common Multiple of 75,77,415 with GCF Formula

Least Common Multiple of 75,77,415 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 75,77,415 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(75,77,415) = 1

common factors(in case of two or more numbers have common factors) = 5

GCF(75,77,415) x common factors =1 x 5 = 5

LCM(75,77,415) = ( 75 × 77 × 415 ) / 5

LCM(75,77,415) = 2396625 / 5

LCM(75,77,415) = 479325


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 106/75, 409/77, 559/415

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 106/75, 409/77, 559/415?

Answer: GCF of Numerators as per given numbers 106/75, 409/77, 559/415 is

GCF of Numerators i.e. for 106,409,559 is 1

LCM of denominators i.e. for 75,77,415 is 479325.

Thus, GCF of Fractions is 1/479325.Finally, GCF of Fractions for 106/75, 409/77, 559/415 is 1/479325.