How to Find GCF of 13/52, 14/50, 259/514?

GCF of 13/52, 14/50, 259/514

Created By : Veerendra
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023

Use our free GCF of Fractions Calculator tool to compute the GCF of 13/52, 14/50, 259/514 i.e 1/334100 easily. The following is the detailed procedure to determine the greatest common factor of fractions 13/52, 14/50, 259/514.

Enter two or more fractions separated by "commas"

Ex: 2/3, 5/7 or 3/5, 5/9, 7/3

What is the GCF of 13/52,14/50,259/514?

Given fractions are 13/52,14/50,259/514

To find the GCF of fractions, we have to find the GCF of numerator numbers and LCM of denominator numbers. Its formula is given by

GCF of Fraction = Greatest Common Factor of Numerator/Least Common Multiple of Denominators

In the fractions 13/52,14/50,259/514, numerators are 13,14,259

Denominators are 52,50,514

The GCF of 13,14,259 is 1 .

LCM of 52,50,514 is 334100.

The greatest common factor of 13/52,14/50,259/514 = [GCF of 13,14,259]/[LCM of 52,50,514]= 1/334100

Therefore, the GCF of 13/52,14/50,259/514 is 1/334100.

Greatest Common Factor of 13,14,259

To find the highest common factor of 13,14,259, we have to find the factors of both numbers and list the highest common factor.

The factors of 13 are 1, 13

The factors of 14 are 1, 2, 7, 14

The factors of 259 are 1, 7, 37, 259

The HCF of 13,14,259 is 1.

Lets's calculate GCF of 13,14,259

Greatest Common Factor (GCF) of 13,14,259 By Common Division

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

Greatest Common Factor of 13,14,259 By Matching Biggest Common Factor Method

Now, list down the factors of 13

1,13

Now, list down the factors of 14

1,2,7,14

Now, list down the factors of 259

1,7,37,259

Greatest Common Factor

We found the factors 13,14,259 . The biggest common factor number is the GCF number.
So the greatest common factor 13,14,259 is 1.

Lets's calculate LCM of 52,50,514

Lowest Common Multiple of 52,50,514 using Common Division

2	52, 50, 514
	26, 25, 257

∴ So the LCM of the given numbers is 2 x 26 x 25 x 257 = 334100

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/334100

Therefore, the GCF of Fractions 13/52,14/50,259/514 is 1/334100

Least Common Multiple of 52,50,514 with GCF Formula

The formula of LCM is LCM(a₁,a₂,a₃....,a_n) = ( a₁ × a₂ × a₃ × .... × a_n) / GCF(a₁,a₂,a₃....,a_n) x common factors(if more than 2 numbers have common factors).

We need to calculate greatest common factor of 52,50,514 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(52,50,514) = 2

common factors(in case of two or more numbers have common factors) = 2

GCF(52,50,514) x common factors =2 x 2 = 4

LCM(52,50,514) = ( 52 × 50 × 514 ) / 4

LCM(52,50,514) = 1336400 / 4

LCM(52,50,514) = 334100

GCF of Fractions Calculation Examples

Here are some samples of GCF of Fractions calculations.

FAQs on GCF of Fractions of 13/52, 14/50, 259/514

1. What is the HCF of 13,14,259?

The HCF of 13,14,259 is 1

2. What is the GCF of a fraction?

The GCF of a fraction is defined as the greatest fraction that divides exactly into 2 or more fractions.

3. 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.

4. What is the GCF of Fractions for 13/52, 14/50, 259/514?

Answer: GCF of Numerators as per given numbers 13/52, 14/50, 259/514 is

GCF of Numerators i.e. for 13,14,259 is 1

LCM of denominators i.e. for 52,50,514 is 334100.

Thus, GCF of Fractions is 1/334100.Finally, GCF of Fractions for 13/52, 14/50, 259/514 is 1/334100.