How to Find GCF of 682/257, 1337/1594?

GCF of 682/257, 1337/1594

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 682/257, 1337/1594 i.e 1/409658 easily. The following is the detailed procedure to determine the greatest common factor of fractions 682/257, 1337/1594.

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 682/257,1337/1594?

Given fractions are 682/257,1337/1594

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 682/257,1337/1594, numerators are 682,1337

Denominators are 257,1594

The GCF of 682,1337 is 1 .

LCM of 257,1594 is 409658.

The greatest common factor of 682/257,1337/1594 = [GCF of 682,1337]/[LCM of 257,1594]= 1/409658

Therefore, the GCF of 682/257,1337/1594 is 1/409658.

Greatest Common Factor of 682,1337

To find the highest common factor of 682,1337, we have to find the factors of both numbers and list the highest common factor.

The factors of 682 are 1, 2, 11, 22, 31, 62, 341, 682

The factors of 1337 are 1, 7, 191, 1337

The HCF of 682,1337 is 1.

Lets's calculate GCF of 682,1337

Greatest Common Factor (GCF) of 682,1337 By Common Division

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

Greatest Common Factor of 682,1337 By Matching Biggest Common Factor Method

Now, list down the factors of 682

1,2,11,22,31,62,341,682

Now, list down the factors of 1337

1,7,191,1337

Greatest Common Factor

We found the factors 682,1337 . The biggest common factor number is the GCF number.
So the greatest common factor 682,1337 is 1.

Lets's calculate LCM of 257,1594

Lowest Common Multiple of 257,1594 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 409658

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/409658

Therefore, the GCF of Fractions 682/257,1337/1594 is 1/409658

Least Common Multiple of 257,1594 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 257,1594 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(257,1594) = 1

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

GCF(257,1594) x common factors =1 x 1 = 1

LCM(257,1594) = ( 257 × 1594 ) / 1

LCM(257,1594) = 409658 / 1

LCM(257,1594) = 409658

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FAQs on GCF of Fractions of 682/257, 1337/1594

1. What is the HCF of 682,1337?

The HCF of 682,1337 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 682/257, 1337/1594?

Answer: GCF of Numerators as per given numbers 682/257, 1337/1594 is

GCF of Numerators i.e. for 682,1337 is 1

LCM of denominators i.e. for 257,1594 is 409658.

Thus, GCF of Fractions is 1/409658.Finally, GCF of Fractions for 682/257, 1337/1594 is 1/409658.