How to Find GCF of 13/34, 26/16, 541/259?

GCF of 13/34, 26/16, 541/259

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 13/34, 26/16, 541/259 i.e 1/70448 easily. The following is the detailed procedure to determine the greatest common factor of fractions 13/34, 26/16, 541/259.

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 13/34,26/16,541/259?

Given fractions are 13/34,26/16,541/259

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 13/34,26/16,541/259, numerators are 13,26,541

Denominators are 34,16,259

The GCF of 13,26,541 is 1 .

LCM of 34,16,259 is 70448.

The greatest common factor of 13/34,26/16,541/259 = [GCF of 13,26,541]/[LCM of 34,16,259]= 1/70448

Therefore, the GCF of 13/34,26/16,541/259 is 1/70448.

Greatest Common Factor of 13,26,541

To find the highest common factor of 13,26,541, 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 26 are 1, 2, 13, 26

The factors of 541 are 1, 541

The HCF of 13,26,541 is 1.

Lets's calculate GCF of 13,26,541

Greatest Common Factor (GCF) of 13,26,541 By Common Division

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

Greatest Common Factor of 13,26,541 By Matching Biggest Common Factor Method

Now, list down the factors of 13

1,13

Now, list down the factors of 26

1,2,13,26

Now, list down the factors of 541

1,541

Greatest Common Factor

We found the factors 13,26,541 . The biggest common factor number is the GCF number.
So the greatest common factor 13,26,541 is 1.

Lets's calculate LCM of 34,16,259

Lowest Common Multiple of 34,16,259 using Common Division

2	34, 16, 259
	17, 8, 259

∴ So the LCM of the given numbers is 2 x 17 x 8 x 259 = 70448

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/70448

Therefore, the GCF of Fractions 13/34,26/16,541/259 is 1/70448

Least Common Multiple of 34,16,259 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 34,16,259 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(34,16,259) = 1

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

GCF(34,16,259) x common factors =1 x 2 = 2

LCM(34,16,259) = ( 34 × 16 × 259 ) / 2

LCM(34,16,259) = 140896 / 2

LCM(34,16,259) = 70448

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FAQs on GCF of Fractions of 13/34, 26/16, 541/259

1. What is the HCF of 13,26,541?

The HCF of 13,26,541 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 13/34, 26/16, 541/259?

Answer: GCF of Numerators as per given numbers 13/34, 26/16, 541/259 is

GCF of Numerators i.e. for 13,26,541 is 1

LCM of denominators i.e. for 34,16,259 is 70448.

Thus, GCF of Fractions is 1/70448.Finally, GCF of Fractions for 13/34, 26/16, 541/259 is 1/70448.