How to Find GCF of 710/728, 7708/5652?

GCF of 710/728, 7708/5652

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 710/728, 7708/5652 i.e 2/1028664 easily. The following is the detailed procedure to determine the greatest common factor of fractions 710/728, 7708/5652.

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 710/728,7708/5652?

Given fractions are 710/728,7708/5652

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 710/728,7708/5652, numerators are 710,7708

Denominators are 728,5652

The GCF of 710,7708 is 2 .

LCM of 728,5652 is 1028664.

The greatest common factor of 710/728,7708/5652 = [GCF of 710,7708]/[LCM of 728,5652]= 2/1028664

Therefore, the GCF of 710/728,7708/5652 is 2/1028664.

Greatest Common Factor of 710,7708

To find the highest common factor of 710,7708, we have to find the factors of both numbers and list the highest common factor.

The factors of 710 are 1, 2, 5, 10, 71, 142, 355, 710

The factors of 7708 are 1, 2, 4, 41, 47, 82, 94, 164, 188, 1927, 3854, 7708

The HCF of 710,7708 is 2.

Lets's calculate GCF of 710,7708

Greatest Common Factor (GCF) of 710,7708 By Common Division

2	710, 7708
	355, 3854

∴ So the GCF of the given numbers is 2 = 2

Greatest Common Factor of 710,7708 By Matching Biggest Common Factor Method

Now, list down the factors of 710

1,2,5,10,71,142,355,710

Now, list down the factors of 7708

1,2,4,41,47,82,94,164,188,1927,3854,7708

Greatest Common Factor

We found the factors 710,7708 . The biggest common factor number is the GCF number.
So the greatest common factor 710,7708 is 2.

Lets's calculate LCM of 728,5652

Lowest Common Multiple of 728,5652 using Common Division

2	728, 5652
2	364, 2826
	182, 1413

∴ So the LCM of the given numbers is 2 x 2 x 182 x 1413 = 1028664

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/1028664

Therefore, the GCF of Fractions 710/728,7708/5652 is 2/1028664

Least Common Multiple of 728,5652 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 728,5652 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(728,5652) = 4

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

GCF(728,5652) x common factors =4 x 1 = 4

LCM(728,5652) = ( 728 × 5652 ) / 4

LCM(728,5652) = 4114656 / 4

LCM(728,5652) = 1028664

GCF of Fractions Calculation Examples

Here are some samples of GCF of Fractions calculations.

FAQs on GCF of Fractions of 710/728, 7708/5652

1. What is the HCF of 710,7708?

The HCF of 710,7708 is 2

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 710/728, 7708/5652?

Answer: GCF of Numerators as per given numbers 710/728, 7708/5652 is

GCF of Numerators i.e. for 710,7708 is 2

LCM of denominators i.e. for 728,5652 is 1028664.

Thus, GCF of Fractions is 2/1028664.Finally, GCF of Fractions for 710/728, 7708/5652 is 2/1028664.