How to Find GCF of 3982/994, 8074/1666?

GCF of 3982/994, 8074/1666

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 3982/994, 8074/1666 i.e 22/118286 easily. The following is the detailed procedure to determine the greatest common factor of fractions 3982/994, 8074/1666.

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 3982/994,8074/1666?

Given fractions are 3982/994,8074/1666

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 3982/994,8074/1666, numerators are 3982,8074

Denominators are 994,1666

The GCF of 3982,8074 is 22 .

LCM of 994,1666 is 118286.

The greatest common factor of 3982/994,8074/1666 = [GCF of 3982,8074]/[LCM of 994,1666]= 22/118286

Therefore, the GCF of 3982/994,8074/1666 is 22/118286.

Greatest Common Factor of 3982,8074

To find the highest common factor of 3982,8074, we have to find the factors of both numbers and list the highest common factor.

The factors of 3982 are 1, 2, 11, 22, 181, 362, 1991, 3982

The factors of 8074 are 1, 2, 11, 22, 367, 734, 4037, 8074

The HCF of 3982,8074 is 22.

Lets's calculate GCF of 3982,8074

Greatest Common Factor (GCF) of 3982,8074 By Common Division

2	3982, 8074
11	1991, 4037
	181, 367

∴ So the GCF of the given numbers is 2 x 11 = 22

Greatest Common Factor of 3982,8074 By Matching Biggest Common Factor Method

Now, list down the factors of 3982

1,2,11,22,181,362,1991,3982

Now, list down the factors of 8074

1,2,11,22,367,734,4037,8074

Greatest Common Factor

We found the factors 3982,8074 . The biggest common factor number is the GCF number.
So the greatest common factor 3982,8074 is 22.

Lets's calculate LCM of 994,1666

Lowest Common Multiple of 994,1666 using Common Division

2	994, 1666
7	497, 833
	71, 119

∴ So the LCM of the given numbers is 2 x 7 x 71 x 119 = 118286

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 22/118286

Therefore, the GCF of Fractions 3982/994,8074/1666 is 22/118286

Least Common Multiple of 994,1666 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 994,1666 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(994,1666) = 14

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

GCF(994,1666) x common factors =14 x 1 = 14

LCM(994,1666) = ( 994 × 1666 ) / 14

LCM(994,1666) = 1656004 / 14

LCM(994,1666) = 118286

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FAQs on GCF of Fractions of 3982/994, 8074/1666

1. What is the HCF of 3982,8074?

The HCF of 3982,8074 is 22

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 3982/994, 8074/1666?

Answer: GCF of Numerators as per given numbers 3982/994, 8074/1666 is

GCF of Numerators i.e. for 3982,8074 is 22

LCM of denominators i.e. for 994,1666 is 118286.

Thus, GCF of Fractions is 22/118286.Finally, GCF of Fractions for 3982/994, 8074/1666 is 22/118286.