How to Find GCF of 13/269, 9867/7841?

GCF of 13/269, 9867/7841

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 13/269, 9867/7841 i.e 13/2109229 easily. The following is the detailed procedure to determine the greatest common factor of fractions 13/269, 9867/7841.

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 13/269,9867/7841?

Given fractions are 13/269,9867/7841

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 13/269,9867/7841, numerators are 13,9867

Denominators are 269,7841

The GCF of 13,9867 is 13 .

LCM of 269,7841 is 2109229.

The greatest common factor of 13/269,9867/7841 = [GCF of 13,9867]/[LCM of 269,7841]= 13/2109229

Therefore, the GCF of 13/269,9867/7841 is 13/2109229.

Greatest Common Factor of 13,9867

To find the highest common factor of 13,9867, 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 9867 are 1, 3, 11, 13, 23, 33, 39, 69, 143, 253, 299, 429, 759, 897, 3289, 9867

The HCF of 13,9867 is 13.

Lets's calculate GCF of 13,9867

Greatest Common Factor (GCF) of 13,9867 By Common Division

13	13, 9867
	1, 759

∴ So the GCF of the given numbers is 13 = 13

Greatest Common Factor of 13,9867 By Matching Biggest Common Factor Method

Now, list down the factors of 13

1,13

Now, list down the factors of 9867

1,3,11,13,23,33,39,69,143,253,299,429,759,897,3289,9867

Greatest Common Factor

We found the factors 13,9867 . The biggest common factor number is the GCF number.
So the greatest common factor 13,9867 is 13.

Lets's calculate LCM of 269,7841

Lowest Common Multiple of 269,7841 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 2109229

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 13/2109229

Therefore, the GCF of Fractions 13/269,9867/7841 is 13/2109229

Least Common Multiple of 269,7841 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 269,7841 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(269,7841) = 1

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

GCF(269,7841) x common factors =1 x 1 = 1

LCM(269,7841) = ( 269 × 7841 ) / 1

LCM(269,7841) = 2109229 / 1

LCM(269,7841) = 2109229

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FAQs on GCF of Fractions of 13/269, 9867/7841

1. What is the HCF of 13,9867?

The HCF of 13,9867 is 13

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 13/269, 9867/7841?

Answer: GCF of Numerators as per given numbers 13/269, 9867/7841 is

GCF of Numerators i.e. for 13,9867 is 13

LCM of denominators i.e. for 269,7841 is 2109229.

Thus, GCF of Fractions is 13/2109229.Finally, GCF of Fractions for 13/269, 9867/7841 is 13/2109229.