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GCF of 517/794, 854/208

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 517/794, 854/208 i.e 1/82576 easily. The following is the detailed procedure to determine the greatest common factor of fractions 517/794, 854/208.

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 517/794,854/208?

Given fractions are 517/794,854/208

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 517/794,854/208, numerators are 517,854

Denominators are 794,208

The GCF of 517,854 is 1 .

LCM of 794,208 is 82576.

The greatest common factor of 517/794,854/208 = [GCF of 517,854]/[LCM of 794,208]= 1/82576

Therefore, the GCF of 517/794,854/208 is 1/82576.

Greatest Common Factor of 517,854

To find the highest common factor of 517,854, we have to find the factors of both numbers and list the highest common factor.

The factors of 517 are 1, 11, 47, 517

The factors of 854 are 1, 2, 7, 14, 61, 122, 427, 854

The HCF of 517,854 is 1.

Lets's calculate GCF of 517,854

Greatest Common Factor (GCF) of 517,854 By Common Division

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

Greatest Common Factor of 517,854 By Matching Biggest Common Factor Method

Greatest Common Factor of 517,854 By Matching Biggest Common Factor Method

Now, list down the factors of 517

:

1,11,47,517

Now, list down the factors of 854

:

1,2,7,14,61,122,427,854

Greatest Common Factor

We found the factors 517,854 . The biggest common factor number is the GCF number.
So the greatest common factor 517,854 is 1.

Lets's calculate LCM of 794,208

Lowest Common Multiple of 794,208 using Common Division

2 794, 208
397, 104

∴ So the LCM of the given numbers is 2 x 397 x 104 = 82576

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/82576

Therefore, the GCF of Fractions 517/794,854/208 is 1/82576

Least Common Multiple of 794,208 with GCF Formula

Least Common Multiple of 794,208 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 794,208 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(794,208) = 2

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

GCF(794,208) x common factors =2 x 1 = 2

LCM(794,208) = ( 794 × 208 ) / 2

LCM(794,208) = 165152 / 2

LCM(794,208) = 82576


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FAQs on GCF of Fractions of 517/794, 854/208

1. What is the HCF of 517,854?

The HCF of 517,854 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 517/794, 854/208?

Answer: GCF of Numerators as per given numbers 517/794, 854/208 is

GCF of Numerators i.e. for 517,854 is 1

LCM of denominators i.e. for 794,208 is 82576.

Thus, GCF of Fractions is 1/82576.Finally, GCF of Fractions for 517/794, 854/208 is 1/82576.