How to Find GCF of 494/320, 2405/778?

GCF of 494/320, 2405/778

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 494/320, 2405/778 i.e 13/124480 easily. The following is the detailed procedure to determine the greatest common factor of fractions 494/320, 2405/778.

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 494/320,2405/778?

Given fractions are 494/320,2405/778

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 494/320,2405/778, numerators are 494,2405

Denominators are 320,778

The GCF of 494,2405 is 13 .

LCM of 320,778 is 124480.

The greatest common factor of 494/320,2405/778 = [GCF of 494,2405]/[LCM of 320,778]= 13/124480

Therefore, the GCF of 494/320,2405/778 is 13/124480.

Greatest Common Factor of 494,2405

To find the highest common factor of 494,2405, we have to find the factors of both numbers and list the highest common factor.

The factors of 494 are 1, 2, 13, 19, 26, 38, 247, 494

The factors of 2405 are 1, 5, 13, 37, 65, 185, 481, 2405

The HCF of 494,2405 is 13.

Lets's calculate GCF of 494,2405

Greatest Common Factor (GCF) of 494,2405 By Common Division

13	494, 2405
	38, 185

∴ So the GCF of the given numbers is 13 = 13

Greatest Common Factor of 494,2405 By Matching Biggest Common Factor Method

Now, list down the factors of 494

1,2,13,19,26,38,247,494

Now, list down the factors of 2405

1,5,13,37,65,185,481,2405

Greatest Common Factor

We found the factors 494,2405 . The biggest common factor number is the GCF number.
So the greatest common factor 494,2405 is 13.

Lets's calculate LCM of 320,778

Lowest Common Multiple of 320,778 using Common Division

2	320, 778
	160, 389

∴ So the LCM of the given numbers is 2 x 160 x 389 = 124480

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 13/124480

Therefore, the GCF of Fractions 494/320,2405/778 is 13/124480

Least Common Multiple of 320,778 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 320,778 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(320,778) = 2

common factors(in case of two or more numbers have common factors) = 1

GCF(320,778) x common factors =2 x 1 = 2

LCM(320,778) = ( 320 × 778 ) / 2

LCM(320,778) = 248960 / 2

LCM(320,778) = 124480

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FAQs on GCF of Fractions of 494/320, 2405/778

1. What is the HCF of 494,2405?

The HCF of 494,2405 is 13

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 494/320, 2405/778?

Answer: GCF of Numerators as per given numbers 494/320, 2405/778 is

GCF of Numerators i.e. for 494,2405 is 13

LCM of denominators i.e. for 320,778 is 124480.

Thus, GCF of Fractions is 13/124480.Finally, GCF of Fractions for 494/320, 2405/778 is 13/124480.