How to Find GCF of 82/164, 74/772, 631/931?

GCF of 82/164, 74/772, 631/931

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 82/164, 74/772, 631/931 i.e 1/29468012 easily. The following is the detailed procedure to determine the greatest common factor of fractions 82/164, 74/772, 631/931.

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 82/164,74/772,631/931?

Given fractions are 82/164,74/772,631/931

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 82/164,74/772,631/931, numerators are 82,74,631

Denominators are 164,772,931

The GCF of 82,74,631 is 1 .

LCM of 164,772,931 is 29468012.

The greatest common factor of 82/164,74/772,631/931 = [GCF of 82,74,631]/[LCM of 164,772,931]= 1/29468012

Therefore, the GCF of 82/164,74/772,631/931 is 1/29468012.

Greatest Common Factor of 82,74,631

To find the highest common factor of 82,74,631, we have to find the factors of both numbers and list the highest common factor.

The factors of 82 are 1, 2, 41, 82

The factors of 74 are 1, 2, 37, 74

The factors of 631 are 1, 631

The HCF of 82,74,631 is 1.

Lets's calculate GCF of 82,74,631

Greatest Common Factor (GCF) of 82,74,631 By Common Division

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

Greatest Common Factor of 82,74,631 By Matching Biggest Common Factor Method

Now, list down the factors of 82

1,2,41,82

Now, list down the factors of 74

1,2,37,74

Now, list down the factors of 631

1,631

Greatest Common Factor

We found the factors 82,74,631 . The biggest common factor number is the GCF number.
So the greatest common factor 82,74,631 is 1.

Lets's calculate LCM of 164,772,931

Lowest Common Multiple of 164,772,931 using Common Division

2	164, 772, 931
2	82, 386, 931
	41, 193, 931

∴ So the LCM of the given numbers is 2 x 2 x 41 x 193 x 931 = 29468012

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/29468012

Therefore, the GCF of Fractions 82/164,74/772,631/931 is 1/29468012

Least Common Multiple of 164,772,931 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 164,772,931 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(164,772,931) = 1

common factors(in case of two or more numbers have common factors) = 4

GCF(164,772,931) x common factors =1 x 4 = 4

LCM(164,772,931) = ( 164 × 772 × 931 ) / 4

LCM(164,772,931) = 117872048 / 4

LCM(164,772,931) = 29468012

GCF of Fractions Calculation Examples

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FAQs on GCF of Fractions of 82/164, 74/772, 631/931

1. What is the HCF of 82,74,631?

The HCF of 82,74,631 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 82/164, 74/772, 631/931?

Answer: GCF of Numerators as per given numbers 82/164, 74/772, 631/931 is

GCF of Numerators i.e. for 82,74,631 is 1

LCM of denominators i.e. for 164,772,931 is 29468012.

Thus, GCF of Fractions is 1/29468012.Finally, GCF of Fractions for 82/164, 74/772, 631/931 is 1/29468012.