Greatest Common Factor of 214/13, 304/14, 566/336

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

GCF of 214/13, 304/14, 566/336

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 214/13,304/14,566/336

Given fractions are 214/13,304/14,566/336

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 214,304,566

Greatest Common Factor of Numerators i.e. GCF of 214,304,566 is 2 .

LCM of Denominators means LCM of 13,14,336 as per the given fractions.

LCM of 13,14,336 is 4368 as it is the smallest common factor for both these numbers.

Lets's calculate GCF of 214,304,566

GCF of Fractions 214/13,304/14,566/336 is 2/4368

2 214, 304, 566
107, 152, 283

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

Greatest Common Factor of 214,304,566 By Matching Biggest Common Factor Method

Greatest Common Factor of 214,304,566 By Matching Biggest Common Factor Method

Factors of 214

List of positive integer factors of 214 that divides 214 without a remainder.

1,2,107,214

Factors of 304

List of positive integer factors of 304 that divides 304 without a remainder.

1,2,4,8,16,19,38,76,152,304

Factors of 566

List of positive integer factors of 566 that divides 566 without a remainder.

1,2,283,566

Greatest Common Factor

We found the factors 214,304,566 . The biggest common factor number is the GCF number.
So the greatest common factor 214,304,566 is 2.

Lets's calculate LCM of 13,14,336

2 13, 14, 336
7 13, 7, 168
13, 1, 24

∴ So the LCM of the given numbers is 2 x 7 x 13 x 1 x 24 = 4368

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/4368

Therefore, the GCF of Fractions 214/13,304/14,566/336 is 2/4368

Least Common Multiple of 13,14,336 with GCF Formula

Least Common Multiple of 13,14,336 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 13,14,336 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(13,14,336) = 1

common factors(in case of two or more numbers have common factors) = 14

GCF(13,14,336) x common factors =1 x 14 = 14

LCM(13,14,336) = ( 13 × 14 × 336 ) / 14

LCM(13,14,336) = 61152 / 14

LCM(13,14,336) = 4368


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 214/13, 304/14, 566/336

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 214/13, 304/14, 566/336?

Answer: GCF of Numerators as per given numbers 214/13, 304/14, 566/336 is

GCF of Numerators i.e. for 214,304,566 is 2

LCM of denominators i.e. for 13,14,336 is 4368.

Thus, GCF of Fractions is 2/4368.Finally, GCF of Fractions for 214/13, 304/14, 566/336 is 2/4368.