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GCF of 765/231, 926/714

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 765/231, 926/714 i.e 1/7854 easily. The following is the detailed procedure to determine the greatest common factor of fractions 765/231, 926/714.

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 765/231,926/714?

Given fractions are 765/231,926/714

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 765/231,926/714, numerators are 765,926

Denominators are 231,714

The GCF of 765,926 is 1 .

LCM of 231,714 is 7854.

The greatest common factor of 765/231,926/714 = [GCF of 765,926]/[LCM of 231,714]= 1/7854

Therefore, the GCF of 765/231,926/714 is 1/7854.

Greatest Common Factor of 765,926

To find the highest common factor of 765,926, we have to find the factors of both numbers and list the highest common factor.

The factors of 765 are 1, 3, 5, 9, 15, 17, 45, 51, 85, 153, 255, 765

The factors of 926 are 1, 2, 463, 926

The HCF of 765,926 is 1.

Lets's calculate GCF of 765,926

Greatest Common Factor (GCF) of 765,926 By Common Division

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

Greatest Common Factor of 765,926 By Matching Biggest Common Factor Method

Greatest Common Factor of 765,926 By Matching Biggest Common Factor Method

Now, list down the factors of 765

:

1,3,5,9,15,17,45,51,85,153,255,765

Now, list down the factors of 926

:

1,2,463,926

Greatest Common Factor

We found the factors 765,926 . The biggest common factor number is the GCF number.
So the greatest common factor 765,926 is 1.

Lets's calculate LCM of 231,714

Lowest Common Multiple of 231,714 using Common Division

3 231, 714
7 77, 238
11, 34

∴ So the LCM of the given numbers is 3 x 7 x 11 x 34 = 7854

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/7854

Therefore, the GCF of Fractions 765/231,926/714 is 1/7854

Least Common Multiple of 231,714 with GCF Formula

Least Common Multiple of 231,714 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 231,714 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(231,714) = 21

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

GCF(231,714) x common factors =21 x 1 = 21

LCM(231,714) = ( 231 × 714 ) / 21

LCM(231,714) = 164934 / 21

LCM(231,714) = 7854


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FAQs on GCF of Fractions of 765/231, 926/714

1. What is the HCF of 765,926?

The HCF of 765,926 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 765/231, 926/714?

Answer: GCF of Numerators as per given numbers 765/231, 926/714 is

GCF of Numerators i.e. for 765,926 is 1

LCM of denominators i.e. for 231,714 is 7854.

Thus, GCF of Fractions is 1/7854.Finally, GCF of Fractions for 765/231, 926/714 is 1/7854.