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GCF of 434/766, 1323/686

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 434/766, 1323/686 i.e 7/262738 easily. The following is the detailed procedure to determine the greatest common factor of fractions 434/766, 1323/686.

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 434/766,1323/686?

Given fractions are 434/766,1323/686

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 434/766,1323/686, numerators are 434,1323

Denominators are 766,686

The GCF of 434,1323 is 7 .

LCM of 766,686 is 262738.

The greatest common factor of 434/766,1323/686 = [GCF of 434,1323]/[LCM of 766,686]= 7/262738

Therefore, the GCF of 434/766,1323/686 is 7/262738.

Greatest Common Factor of 434,1323

To find the highest common factor of 434,1323, we have to find the factors of both numbers and list the highest common factor.

The factors of 434 are 1, 2, 7, 14, 31, 62, 217, 434

The factors of 1323 are 1, 3, 7, 9, 21, 27, 49, 63, 147, 189, 441, 1323

The HCF of 434,1323 is 7.

Lets's calculate GCF of 434,1323

Greatest Common Factor (GCF) of 434,1323 By Common Division

7 434, 1323
62, 189

∴ So the GCF of the given numbers is 7 = 7

Greatest Common Factor of 434,1323 By Matching Biggest Common Factor Method

Greatest Common Factor of 434,1323 By Matching Biggest Common Factor Method

Now, list down the factors of 434

:

1,2,7,14,31,62,217,434

Now, list down the factors of 1323

:

1,3,7,9,21,27,49,63,147,189,441,1323

Greatest Common Factor

We found the factors 434,1323 . The biggest common factor number is the GCF number.
So the greatest common factor 434,1323 is 7.

Lets's calculate LCM of 766,686

Lowest Common Multiple of 766,686 using Common Division

2 766, 686
383, 343

∴ So the LCM of the given numbers is 2 x 383 x 343 = 262738

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 7/262738

Therefore, the GCF of Fractions 434/766,1323/686 is 7/262738

Least Common Multiple of 766,686 with GCF Formula

Least Common Multiple of 766,686 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 766,686 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(766,686) = 2

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

GCF(766,686) x common factors =2 x 1 = 2

LCM(766,686) = ( 766 × 686 ) / 2

LCM(766,686) = 525476 / 2

LCM(766,686) = 262738


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FAQs on GCF of Fractions of 434/766, 1323/686

1. What is the HCF of 434,1323?

The HCF of 434,1323 is 7

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 434/766, 1323/686?

Answer: GCF of Numerators as per given numbers 434/766, 1323/686 is

GCF of Numerators i.e. for 434,1323 is 7

LCM of denominators i.e. for 766,686 is 262738.

Thus, GCF of Fractions is 7/262738.Finally, GCF of Fractions for 434/766, 1323/686 is 7/262738.