How to Find GCF of 41/71, 54/38, 742/652?

GCF of 41/71, 54/38, 742/652

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 41/71, 54/38, 742/652 i.e 1/879548 easily. The following is the detailed procedure to determine the greatest common factor of fractions 41/71, 54/38, 742/652.

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 41/71,54/38,742/652?

Given fractions are 41/71,54/38,742/652

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 41/71,54/38,742/652, numerators are 41,54,742

Denominators are 71,38,652

The GCF of 41,54,742 is 1 .

LCM of 71,38,652 is 879548.

The greatest common factor of 41/71,54/38,742/652 = [GCF of 41,54,742]/[LCM of 71,38,652]= 1/879548

Therefore, the GCF of 41/71,54/38,742/652 is 1/879548.

Greatest Common Factor of 41,54,742

To find the highest common factor of 41,54,742, we have to find the factors of both numbers and list the highest common factor.

The factors of 41 are 1, 41

The factors of 54 are 1, 2, 3, 6, 9, 18, 27, 54

The factors of 742 are 1, 2, 7, 14, 53, 106, 371, 742

The HCF of 41,54,742 is 1.

Lets's calculate GCF of 41,54,742

Greatest Common Factor (GCF) of 41,54,742 By Common Division

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

Greatest Common Factor of 41,54,742 By Matching Biggest Common Factor Method

Now, list down the factors of 41

1,41

Now, list down the factors of 54

1,2,3,6,9,18,27,54

Now, list down the factors of 742

1,2,7,14,53,106,371,742

Greatest Common Factor

We found the factors 41,54,742 . The biggest common factor number is the GCF number.
So the greatest common factor 41,54,742 is 1.

Lets's calculate LCM of 71,38,652

Lowest Common Multiple of 71,38,652 using Common Division

2	71, 38, 652
	71, 19, 326

∴ So the LCM of the given numbers is 2 x 71 x 19 x 326 = 879548

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/879548

Therefore, the GCF of Fractions 41/71,54/38,742/652 is 1/879548

Least Common Multiple of 71,38,652 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 71,38,652 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(71,38,652) = 1

common factors(in case of two or more numbers have common factors) = 2

GCF(71,38,652) x common factors =1 x 2 = 2

LCM(71,38,652) = ( 71 × 38 × 652 ) / 2

LCM(71,38,652) = 1759096 / 2

LCM(71,38,652) = 879548

GCF of Fractions Calculation Examples

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FAQs on GCF of Fractions of 41/71, 54/38, 742/652

1. What is the HCF of 41,54,742?

The HCF of 41,54,742 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 41/71, 54/38, 742/652?

Answer: GCF of Numerators as per given numbers 41/71, 54/38, 742/652 is

GCF of Numerators i.e. for 41,54,742 is 1

LCM of denominators i.e. for 71,38,652 is 879548.

Thus, GCF of Fractions is 1/879548.Finally, GCF of Fractions for 41/71, 54/38, 742/652 is 1/879548.