How to Find GCF of 32/81, 13/77, 43/242?

GCF of 32/81, 13/77, 43/242

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 32/81, 13/77, 43/242 i.e 1/137214 easily. The following is the detailed procedure to determine the greatest common factor of fractions 32/81, 13/77, 43/242.

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 32/81,13/77,43/242?

Given fractions are 32/81,13/77,43/242

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 32/81,13/77,43/242, numerators are 32,13,43

Denominators are 81,77,242

The GCF of 32,13,43 is 1 .

LCM of 81,77,242 is 137214.

The greatest common factor of 32/81,13/77,43/242 = [GCF of 32,13,43]/[LCM of 81,77,242]= 1/137214

Therefore, the GCF of 32/81,13/77,43/242 is 1/137214.

Greatest Common Factor of 32,13,43

To find the highest common factor of 32,13,43, we have to find the factors of both numbers and list the highest common factor.

The factors of 32 are 1, 2, 4, 8, 16, 32

The factors of 13 are 1, 13

The factors of 43 are 1, 43

The HCF of 32,13,43 is 1.

Lets's calculate GCF of 32,13,43

Greatest Common Factor (GCF) of 32,13,43 By Common Division

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

Greatest Common Factor of 32,13,43 By Matching Biggest Common Factor Method

Now, list down the factors of 32

1,2,4,8,16,32

Now, list down the factors of 13

1,13

Now, list down the factors of 43

1,43

Greatest Common Factor

We found the factors 32,13,43 . The biggest common factor number is the GCF number.
So the greatest common factor 32,13,43 is 1.

Lets's calculate LCM of 81,77,242

Lowest Common Multiple of 81,77,242 using Common Division

11	81, 77, 242
	81, 7, 22

∴ So the LCM of the given numbers is 11 x 81 x 7 x 22 = 137214

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/137214

Therefore, the GCF of Fractions 32/81,13/77,43/242 is 1/137214

Least Common Multiple of 81,77,242 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 81,77,242 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(81,77,242) = 1

common factors(in case of two or more numbers have common factors) = 11

GCF(81,77,242) x common factors =1 x 11 = 11

LCM(81,77,242) = ( 81 × 77 × 242 ) / 11

LCM(81,77,242) = 1509354 / 11

LCM(81,77,242) = 137214

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FAQs on GCF of Fractions of 32/81, 13/77, 43/242

1. What is the HCF of 32,13,43?

The HCF of 32,13,43 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 32/81, 13/77, 43/242?

Answer: GCF of Numerators as per given numbers 32/81, 13/77, 43/242 is

GCF of Numerators i.e. for 32,13,43 is 1

LCM of denominators i.e. for 81,77,242 is 137214.

Thus, GCF of Fractions is 1/137214.Finally, GCF of Fractions for 32/81, 13/77, 43/242 is 1/137214.