How to Find GCF of 6981/922, 1739/1406?

GCF of 6981/922, 1739/1406

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 6981/922, 1739/1406 i.e 1/648166 easily. The following is the detailed procedure to determine the greatest common factor of fractions 6981/922, 1739/1406.

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 6981/922,1739/1406?

Given fractions are 6981/922,1739/1406

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 6981/922,1739/1406, numerators are 6981,1739

Denominators are 922,1406

The GCF of 6981,1739 is 1 .

LCM of 922,1406 is 648166.

The greatest common factor of 6981/922,1739/1406 = [GCF of 6981,1739]/[LCM of 922,1406]= 1/648166

Therefore, the GCF of 6981/922,1739/1406 is 1/648166.

Greatest Common Factor of 6981,1739

To find the highest common factor of 6981,1739, we have to find the factors of both numbers and list the highest common factor.

The factors of 6981 are 1, 3, 13, 39, 179, 537, 2327, 6981

The factors of 1739 are 1, 37, 47, 1739

The HCF of 6981,1739 is 1.

Lets's calculate GCF of 6981,1739

Greatest Common Factor (GCF) of 6981,1739 By Common Division

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

Greatest Common Factor of 6981,1739 By Matching Biggest Common Factor Method

Now, list down the factors of 6981

1,3,13,39,179,537,2327,6981

Now, list down the factors of 1739

1,37,47,1739

Greatest Common Factor

We found the factors 6981,1739 . The biggest common factor number is the GCF number.
So the greatest common factor 6981,1739 is 1.

Lets's calculate LCM of 922,1406

Lowest Common Multiple of 922,1406 using Common Division

2	922, 1406
	461, 703

∴ So the LCM of the given numbers is 2 x 461 x 703 = 648166

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/648166

Therefore, the GCF of Fractions 6981/922,1739/1406 is 1/648166

Least Common Multiple of 922,1406 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 922,1406 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(922,1406) = 2

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

GCF(922,1406) x common factors =2 x 1 = 2

LCM(922,1406) = ( 922 × 1406 ) / 2

LCM(922,1406) = 1296332 / 2

LCM(922,1406) = 648166

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FAQs on GCF of Fractions of 6981/922, 1739/1406

1. What is the HCF of 6981,1739?

The HCF of 6981,1739 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 6981/922, 1739/1406?

Answer: GCF of Numerators as per given numbers 6981/922, 1739/1406 is

GCF of Numerators i.e. for 6981,1739 is 1

LCM of denominators i.e. for 922,1406 is 648166.

Thus, GCF of Fractions is 1/648166.Finally, GCF of Fractions for 6981/922, 1739/1406 is 1/648166.