How to Find GCF of 27/204, 65/731, 496/394?

GCF of 27/204, 65/731, 496/394

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 27/204, 65/731, 496/394 i.e 1/1728084 easily. The following is the detailed procedure to determine the greatest common factor of fractions 27/204, 65/731, 496/394.

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 27/204,65/731,496/394?

Given fractions are 27/204,65/731,496/394

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 27/204,65/731,496/394, numerators are 27,65,496

Denominators are 204,731,394

The GCF of 27,65,496 is 1 .

LCM of 204,731,394 is 1728084.

The greatest common factor of 27/204,65/731,496/394 = [GCF of 27,65,496]/[LCM of 204,731,394]= 1/1728084

Therefore, the GCF of 27/204,65/731,496/394 is 1/1728084.

Greatest Common Factor of 27,65,496

To find the highest common factor of 27,65,496, we have to find the factors of both numbers and list the highest common factor.

The factors of 27 are 1, 3, 9, 27

The factors of 65 are 1, 5, 13, 65

The factors of 496 are 1, 2, 4, 8, 16, 31, 62, 124, 248, 496

The HCF of 27,65,496 is 1.

Lets's calculate GCF of 27,65,496

Greatest Common Factor (GCF) of 27,65,496 By Common Division

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

Greatest Common Factor of 27,65,496 By Matching Biggest Common Factor Method

Now, list down the factors of 27

1,3,9,27

Now, list down the factors of 65

1,5,13,65

Now, list down the factors of 496

1,2,4,8,16,31,62,124,248,496

Greatest Common Factor

We found the factors 27,65,496 . The biggest common factor number is the GCF number.
So the greatest common factor 27,65,496 is 1.

Lets's calculate LCM of 204,731,394

Lowest Common Multiple of 204,731,394 using Common Division

2	204, 731, 394
17	102, 731, 197
	6, 43, 197

∴ So the LCM of the given numbers is 2 x 17 x 6 x 43 x 197 = 1728084

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/1728084

Therefore, the GCF of Fractions 27/204,65/731,496/394 is 1/1728084

Least Common Multiple of 204,731,394 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 204,731,394 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(204,731,394) = 1

common factors(in case of two or more numbers have common factors) = 34

GCF(204,731,394) x common factors =1 x 34 = 34

LCM(204,731,394) = ( 204 × 731 × 394 ) / 34

LCM(204,731,394) = 58754856 / 34

LCM(204,731,394) = 1728084

GCF of Fractions Calculation Examples

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FAQs on GCF of Fractions of 27/204, 65/731, 496/394

1. What is the HCF of 27,65,496?

The HCF of 27,65,496 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 27/204, 65/731, 496/394?

Answer: GCF of Numerators as per given numbers 27/204, 65/731, 496/394 is

GCF of Numerators i.e. for 27,65,496 is 1

LCM of denominators i.e. for 204,731,394 is 1728084.

Thus, GCF of Fractions is 1/1728084.Finally, GCF of Fractions for 27/204, 65/731, 496/394 is 1/1728084.