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GCF of 269/291, 786/144

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 269/291, 786/144 i.e 1/13968 easily. The following is the detailed procedure to determine the greatest common factor of fractions 269/291, 786/144.

Enter two or more fractions separated by "commas"

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

GCF of:

What is the GCF of 269/291,786/144?

Given fractions are 269/291,786/144

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 269/291,786/144, numerators are 269,786

Denominators are 291,144

The GCF of 269,786 is 1 .

LCM of 291,144 is 13968.

The greatest common factor of 269/291,786/144 = [GCF of 269,786]/[LCM of 291,144]= 1/13968

Therefore, the GCF of 269/291,786/144 is 1/13968.

Greatest Common Factor of 269,786

To find the highest common factor of 269,786, we have to find the factors of both numbers and list the highest common factor.

The factors of 269 are 1, 269

The factors of 786 are 1, 2, 3, 6, 131, 262, 393, 786

The HCF of 269,786 is 1.

Lets's calculate GCF of 269,786

Greatest Common Factor (GCF) of 269,786 By Common Division

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

Greatest Common Factor of 269,786 By Matching Biggest Common Factor Method

Greatest Common Factor of 269,786 By Matching Biggest Common Factor Method

Now, list down the factors of 269

:

1,269

Now, list down the factors of 786

:

1,2,3,6,131,262,393,786

Greatest Common Factor

We found the factors 269,786 . The biggest common factor number is the GCF number.
So the greatest common factor 269,786 is 1.

Lets's calculate LCM of 291,144

Lowest Common Multiple of 291,144 using Common Division

3 291, 144
97, 48

∴ So the LCM of the given numbers is 3 x 97 x 48 = 13968

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/13968

Therefore, the GCF of Fractions 269/291,786/144 is 1/13968

Least Common Multiple of 291,144 with GCF Formula

Least Common Multiple of 291,144 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 291,144 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(291,144) = 3

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

GCF(291,144) x common factors =3 x 1 = 3

LCM(291,144) = ( 291 × 144 ) / 3

LCM(291,144) = 41904 / 3

LCM(291,144) = 13968


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FAQs on GCF of Fractions of 269/291, 786/144

1. What is the HCF of 269,786?

The HCF of 269,786 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 269/291, 786/144?

Answer: GCF of Numerators as per given numbers 269/291, 786/144 is

GCF of Numerators i.e. for 269,786 is 1

LCM of denominators i.e. for 291,144 is 13968.

Thus, GCF of Fractions is 1/13968.Finally, GCF of Fractions for 269/291, 786/144 is 1/13968.