How to Find GCF of 57/40, 82/38, 661/108?

GCF of 57/40, 82/38, 661/108

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 57/40, 82/38, 661/108 i.e 1/20520 easily. The following is the detailed procedure to determine the greatest common factor of fractions 57/40, 82/38, 661/108.

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 57/40,82/38,661/108?

Given fractions are 57/40,82/38,661/108

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 57/40,82/38,661/108, numerators are 57,82,661

Denominators are 40,38,108

The GCF of 57,82,661 is 1 .

LCM of 40,38,108 is 20520.

The greatest common factor of 57/40,82/38,661/108 = [GCF of 57,82,661]/[LCM of 40,38,108]= 1/20520

Therefore, the GCF of 57/40,82/38,661/108 is 1/20520.

Greatest Common Factor of 57,82,661

To find the highest common factor of 57,82,661, we have to find the factors of both numbers and list the highest common factor.

The factors of 57 are 1, 3, 19, 57

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

The factors of 661 are 1, 661

The HCF of 57,82,661 is 1.

Lets's calculate GCF of 57,82,661

Greatest Common Factor (GCF) of 57,82,661 By Common Division

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

Greatest Common Factor of 57,82,661 By Matching Biggest Common Factor Method

Now, list down the factors of 57

1,3,19,57

Now, list down the factors of 82

1,2,41,82

Now, list down the factors of 661

1,661

Greatest Common Factor

We found the factors 57,82,661 . The biggest common factor number is the GCF number.
So the greatest common factor 57,82,661 is 1.

Lets's calculate LCM of 40,38,108

Lowest Common Multiple of 40,38,108 using Common Division

2	40, 38, 108
2	20, 19, 54
	10, 19, 27

∴ So the LCM of the given numbers is 2 x 2 x 10 x 19 x 27 = 20520

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/20520

Therefore, the GCF of Fractions 57/40,82/38,661/108 is 1/20520

Least Common Multiple of 40,38,108 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 40,38,108 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(40,38,108) = 2

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

GCF(40,38,108) x common factors =2 x 4 = 8

LCM(40,38,108) = ( 40 × 38 × 108 ) / 8

LCM(40,38,108) = 164160 / 8

LCM(40,38,108) = 20520

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FAQs on GCF of Fractions of 57/40, 82/38, 661/108

1. What is the HCF of 57,82,661?

The HCF of 57,82,661 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 57/40, 82/38, 661/108?

Answer: GCF of Numerators as per given numbers 57/40, 82/38, 661/108 is

GCF of Numerators i.e. for 57,82,661 is 1

LCM of denominators i.e. for 40,38,108 is 20520.

Thus, GCF of Fractions is 1/20520.Finally, GCF of Fractions for 57/40, 82/38, 661/108 is 1/20520.