Greatest Common Factor of 506/61, 305/21, 105/311

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

GCF of 506/61, 305/21, 105/311

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 506/61,305/21,105/311

Given fractions are 506/61,305/21,105/311

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 506,305,105

Greatest Common Factor of Numerators i.e. GCF of 506,305,105 is 1 .

LCM of Denominators means LCM of 61,21,311 as per the given fractions.

LCM of 61,21,311 is 398391 as it is the smallest common factor for both these numbers.

Lets's calculate GCF of 506,305,105

GCF of Fractions 506/61,305/21,105/311 is 1/398391

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

Greatest Common Factor of 506,305,105 By Matching Biggest Common Factor Method

Greatest Common Factor of 506,305,105 By Matching Biggest Common Factor Method

Factors of 506

List of positive integer factors of 506 that divides 506 without a remainder.

1,2,11,22,23,46,253,506

Factors of 305

List of positive integer factors of 305 that divides 305 without a remainder.

1,5,61,305

Factors of 105

List of positive integer factors of 105 that divides 105 without a remainder.

1,3,5,7,15,21,35,105

Greatest Common Factor

We found the factors 506,305,105 . The biggest common factor number is the GCF number.
So the greatest common factor 506,305,105 is 1.

Lets's calculate LCM of 61,21,311

Given numbers has no common factors except 1. So, there LCM is their product i.e 398391

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/398391

Therefore, the GCF of Fractions 506/61,305/21,105/311 is 1/398391

Least Common Multiple of 61,21,311 with GCF Formula

Least Common Multiple of 61,21,311 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 61,21,311 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(61,21,311) = 1

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

GCF(61,21,311) x common factors =1 x 1 = 1

LCM(61,21,311) = ( 61 × 21 × 311 ) / 1

LCM(61,21,311) = 398391 / 1

LCM(61,21,311) = 398391


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 506/61, 305/21, 105/311

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 506/61, 305/21, 105/311?

Answer: GCF of Numerators as per given numbers 506/61, 305/21, 105/311 is

GCF of Numerators i.e. for 506,305,105 is 1

LCM of denominators i.e. for 61,21,311 is 398391.

Thus, GCF of Fractions is 1/398391.Finally, GCF of Fractions for 506/61, 305/21, 105/311 is 1/398391.