How to Find GCF of 728/781, 533/638?

GCF of 728/781, 533/638

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 728/781, 533/638 i.e 13/45298 easily. The following is the detailed procedure to determine the greatest common factor of fractions 728/781, 533/638.

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 728/781,533/638?

Given fractions are 728/781,533/638

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 728/781,533/638, numerators are 728,533

Denominators are 781,638

The GCF of 728,533 is 13 .

LCM of 781,638 is 45298.

The greatest common factor of 728/781,533/638 = [GCF of 728,533]/[LCM of 781,638]= 13/45298

Therefore, the GCF of 728/781,533/638 is 13/45298.

Greatest Common Factor of 728,533

To find the highest common factor of 728,533, we have to find the factors of both numbers and list the highest common factor.

The factors of 728 are 1, 2, 4, 7, 8, 13, 14, 26, 28, 52, 56, 91, 104, 182, 364, 728

The factors of 533 are 1, 13, 41, 533

The HCF of 728,533 is 13.

Lets's calculate GCF of 728,533

Greatest Common Factor (GCF) of 728,533 By Common Division

13	728, 533
	56, 41

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

Greatest Common Factor of 728,533 By Matching Biggest Common Factor Method

Now, list down the factors of 728

1,2,4,7,8,13,14,26,28,52,56,91,104,182,364,728

Now, list down the factors of 533

1,13,41,533

Greatest Common Factor

We found the factors 728,533 . The biggest common factor number is the GCF number.
So the greatest common factor 728,533 is 13.

Lets's calculate LCM of 781,638

Lowest Common Multiple of 781,638 using Common Division

11	781, 638
	71, 58

∴ So the LCM of the given numbers is 11 x 71 x 58 = 45298

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 13/45298

Therefore, the GCF of Fractions 728/781,533/638 is 13/45298

Least Common Multiple of 781,638 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 781,638 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(781,638) = 11

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

GCF(781,638) x common factors =11 x 1 = 11

LCM(781,638) = ( 781 × 638 ) / 11

LCM(781,638) = 498278 / 11

LCM(781,638) = 45298

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FAQs on GCF of Fractions of 728/781, 533/638

1. What is the HCF of 728,533?

The HCF of 728,533 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 728/781, 533/638?

Answer: GCF of Numerators as per given numbers 728/781, 533/638 is

GCF of Numerators i.e. for 728,533 is 13

LCM of denominators i.e. for 781,638 is 45298.

Thus, GCF of Fractions is 13/45298.Finally, GCF of Fractions for 728/781, 533/638 is 13/45298.