How to Find GCF of 41/86, 204/60, 413/254?

GCF of 41/86, 204/60, 413/254

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 41/86, 204/60, 413/254 i.e 1/327660 easily. The following is the detailed procedure to determine the greatest common factor of fractions 41/86, 204/60, 413/254.

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 41/86,204/60,413/254?

Given fractions are 41/86,204/60,413/254

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 41/86,204/60,413/254, numerators are 41,204,413

Denominators are 86,60,254

The GCF of 41,204,413 is 1 .

LCM of 86,60,254 is 327660.

The greatest common factor of 41/86,204/60,413/254 = [GCF of 41,204,413]/[LCM of 86,60,254]= 1/327660

Therefore, the GCF of 41/86,204/60,413/254 is 1/327660.

Greatest Common Factor of 41,204,413

To find the highest common factor of 41,204,413, 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 204 are 1, 2, 3, 4, 6, 12, 17, 34, 51, 68, 102, 204

The factors of 413 are 1, 7, 59, 413

The HCF of 41,204,413 is 1.

Lets's calculate GCF of 41,204,413

Greatest Common Factor (GCF) of 41,204,413 By Common Division

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

Greatest Common Factor of 41,204,413 By Matching Biggest Common Factor Method

Now, list down the factors of 41

1,41

Now, list down the factors of 204

1,2,3,4,6,12,17,34,51,68,102,204

Now, list down the factors of 413

1,7,59,413

Greatest Common Factor

We found the factors 41,204,413 . The biggest common factor number is the GCF number.
So the greatest common factor 41,204,413 is 1.

Lets's calculate LCM of 86,60,254

Lowest Common Multiple of 86,60,254 using Common Division

2	86, 60, 254
	43, 30, 127

∴ So the LCM of the given numbers is 2 x 43 x 30 x 127 = 327660

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/327660

Therefore, the GCF of Fractions 41/86,204/60,413/254 is 1/327660

Least Common Multiple of 86,60,254 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 86,60,254 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(86,60,254) = 2

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

GCF(86,60,254) x common factors =2 x 2 = 4

LCM(86,60,254) = ( 86 × 60 × 254 ) / 4

LCM(86,60,254) = 1310640 / 4

LCM(86,60,254) = 327660

GCF of Fractions Calculation Examples

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FAQs on GCF of Fractions of 41/86, 204/60, 413/254

1. What is the HCF of 41,204,413?

The HCF of 41,204,413 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 41/86, 204/60, 413/254?

Answer: GCF of Numerators as per given numbers 41/86, 204/60, 413/254 is

GCF of Numerators i.e. for 41,204,413 is 1

LCM of denominators i.e. for 86,60,254 is 327660.

Thus, GCF of Fractions is 1/327660.Finally, GCF of Fractions for 41/86, 204/60, 413/254 is 1/327660.