How to Find GCF of 613/512, 776/728?

GCF of 613/512, 776/728

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 613/512, 776/728 i.e 1/46592 easily. The following is the detailed procedure to determine the greatest common factor of fractions 613/512, 776/728.

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 613/512,776/728?

Given fractions are 613/512,776/728

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 613/512,776/728, numerators are 613,776

Denominators are 512,728

The GCF of 613,776 is 1 .

LCM of 512,728 is 46592.

The greatest common factor of 613/512,776/728 = [GCF of 613,776]/[LCM of 512,728]= 1/46592

Therefore, the GCF of 613/512,776/728 is 1/46592.

Greatest Common Factor of 613,776

To find the highest common factor of 613,776, we have to find the factors of both numbers and list the highest common factor.

The factors of 613 are 1, 613

The factors of 776 are 1, 2, 4, 8, 97, 194, 388, 776

The HCF of 613,776 is 1.

Lets's calculate GCF of 613,776

Greatest Common Factor (GCF) of 613,776 By Common Division

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

Greatest Common Factor of 613,776 By Matching Biggest Common Factor Method

Now, list down the factors of 613

1,613

Now, list down the factors of 776

1,2,4,8,97,194,388,776

Greatest Common Factor

We found the factors 613,776 . The biggest common factor number is the GCF number.
So the greatest common factor 613,776 is 1.

Lets's calculate LCM of 512,728

Lowest Common Multiple of 512,728 using Common Division

2	512, 728
2	256, 364
2	128, 182
	64, 91

∴ So the LCM of the given numbers is 2 x 2 x 2 x 64 x 91 = 46592

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/46592

Therefore, the GCF of Fractions 613/512,776/728 is 1/46592

Least Common Multiple of 512,728 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 512,728 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(512,728) = 8

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

GCF(512,728) x common factors =8 x 1 = 8

LCM(512,728) = ( 512 × 728 ) / 8

LCM(512,728) = 372736 / 8

LCM(512,728) = 46592

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FAQs on GCF of Fractions of 613/512, 776/728

1. What is the HCF of 613,776?

The HCF of 613,776 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 613/512, 776/728?

Answer: GCF of Numerators as per given numbers 613/512, 776/728 is

GCF of Numerators i.e. for 613,776 is 1

LCM of denominators i.e. for 512,728 is 46592.

Thus, GCF of Fractions is 1/46592.Finally, GCF of Fractions for 613/512, 776/728 is 1/46592.