How to Find GCF of 43/421, 61/204, 806/260?

GCF of 43/421, 61/204, 806/260

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 43/421, 61/204, 806/260 i.e 1/5582460 easily. The following is the detailed procedure to determine the greatest common factor of fractions 43/421, 61/204, 806/260.

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 43/421,61/204,806/260?

Given fractions are 43/421,61/204,806/260

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 43/421,61/204,806/260, numerators are 43,61,806

Denominators are 421,204,260

The GCF of 43,61,806 is 1 .

LCM of 421,204,260 is 5582460.

The greatest common factor of 43/421,61/204,806/260 = [GCF of 43,61,806]/[LCM of 421,204,260]= 1/5582460

Therefore, the GCF of 43/421,61/204,806/260 is 1/5582460.

Greatest Common Factor of 43,61,806

To find the highest common factor of 43,61,806, we have to find the factors of both numbers and list the highest common factor.

The factors of 43 are 1, 43

The factors of 61 are 1, 61

The factors of 806 are 1, 2, 13, 26, 31, 62, 403, 806

The HCF of 43,61,806 is 1.

Lets's calculate GCF of 43,61,806

Greatest Common Factor (GCF) of 43,61,806 By Common Division

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

Greatest Common Factor of 43,61,806 By Matching Biggest Common Factor Method

Now, list down the factors of 43

1,43

Now, list down the factors of 61

1,61

Now, list down the factors of 806

1,2,13,26,31,62,403,806

Greatest Common Factor

We found the factors 43,61,806 . The biggest common factor number is the GCF number.
So the greatest common factor 43,61,806 is 1.

Lets's calculate LCM of 421,204,260

Lowest Common Multiple of 421,204,260 using Common Division

2	421, 204, 260
2	421, 102, 130
	421, 51, 65

∴ So the LCM of the given numbers is 2 x 2 x 421 x 51 x 65 = 5582460

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/5582460

Therefore, the GCF of Fractions 43/421,61/204,806/260 is 1/5582460

Least Common Multiple of 421,204,260 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 421,204,260 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(421,204,260) = 1

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

GCF(421,204,260) x common factors =1 x 4 = 4

LCM(421,204,260) = ( 421 × 204 × 260 ) / 4

LCM(421,204,260) = 22329840 / 4

LCM(421,204,260) = 5582460

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FAQs on GCF of Fractions of 43/421, 61/204, 806/260

1. What is the HCF of 43,61,806?

The HCF of 43,61,806 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 43/421, 61/204, 806/260?

Answer: GCF of Numerators as per given numbers 43/421, 61/204, 806/260 is

GCF of Numerators i.e. for 43,61,806 is 1

LCM of denominators i.e. for 421,204,260 is 5582460.

Thus, GCF of Fractions is 1/5582460.Finally, GCF of Fractions for 43/421, 61/204, 806/260 is 1/5582460.