Greatest Common Factor of 209/138, 4213/514

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

GCF of 209/138, 4213/514

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 209/138,4213/514

Given fractions are 209/138,4213/514

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 209,4213

Greatest Common Factor of Numerators i.e. GCF of 209,4213 is 11 .

LCM of Denominators means LCM of 138,514 as per the given fractions.

LCM of 138,514 is 35466 as it is the smallest common factor for both these numbers.

Lets's calculate GCF of 209,4213

GCF of Fractions 209/138,4213/514 is 11/35466

11 209, 4213
19, 383

∴ So the GCF of the given numbers is 11 = 11

Greatest Common Factor of 209,4213 By Matching Biggest Common Factor Method

Greatest Common Factor of 209,4213 By Matching Biggest Common Factor Method

Factors of 209

List of positive integer factors of 209 that divides 209 without a remainder.

1,11,19,209

Factors of 4213

List of positive integer factors of 4213 that divides 4213 without a remainder.

1,11,383,4213

Greatest Common Factor

We found the factors 209,4213 . The biggest common factor number is the GCF number.
So the greatest common factor 209,4213 is 11.

Lets's calculate LCM of 138,514

2 138, 514
69, 257

∴ So the LCM of the given numbers is 2 x 69 x 257 = 35466

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 11/35466

Therefore, the GCF of Fractions 209/138,4213/514 is 11/35466

Least Common Multiple of 138,514 with GCF Formula

Least Common Multiple of 138,514 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 138,514 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(138,514) = 2

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

GCF(138,514) x common factors =2 x 1 = 2

LCM(138,514) = ( 138 × 514 ) / 2

LCM(138,514) = 70932 / 2

LCM(138,514) = 35466


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 209/138, 4213/514

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 209/138, 4213/514?

Answer: GCF of Numerators as per given numbers 209/138, 4213/514 is

GCF of Numerators i.e. for 209,4213 is 11

LCM of denominators i.e. for 138,514 is 35466.

Thus, GCF of Fractions is 11/35466.Finally, GCF of Fractions for 209/138, 4213/514 is 11/35466.