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GCF of 589/522, 713/352

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 589/522, 713/352 i.e 31/91872 easily. The following is the detailed procedure to determine the greatest common factor of fractions 589/522, 713/352.

Enter two or more fractions separated by "commas"

Ex: 2/3, 5/7 or 3/5, 5/9, 7/3

GCF of:

What is the GCF of 589/522,713/352?

Given fractions are 589/522,713/352

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 589/522,713/352, numerators are 589,713

Denominators are 522,352

The GCF of 589,713 is 31 .

LCM of 522,352 is 91872.

The greatest common factor of 589/522,713/352 = [GCF of 589,713]/[LCM of 522,352]= 31/91872

Therefore, the GCF of 589/522,713/352 is 31/91872.

Greatest Common Factor of 589,713

To find the highest common factor of 589,713, we have to find the factors of both numbers and list the highest common factor.

The factors of 589 are 1, 19, 31, 589

The factors of 713 are 1, 23, 31, 713

The HCF of 589,713 is 31.

Lets's calculate GCF of 589,713

Greatest Common Factor (GCF) of 589,713 By Common Division

31 589, 713
19, 23

∴ So the GCF of the given numbers is 31 = 31

Greatest Common Factor of 589,713 By Matching Biggest Common Factor Method

Greatest Common Factor of 589,713 By Matching Biggest Common Factor Method

Now, list down the factors of 589

:

1,19,31,589

Now, list down the factors of 713

:

1,23,31,713

Greatest Common Factor

We found the factors 589,713 . The biggest common factor number is the GCF number.
So the greatest common factor 589,713 is 31.


Lets's calculate LCM of 522,352

Lowest Common Multiple of 522,352 using Common Division

2 522, 352
261, 176

∴ So the LCM of the given numbers is 2 x 261 x 176 = 91872

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 31/91872

Therefore, the GCF of Fractions 589/522,713/352 is 31/91872

Least Common Multiple of 522,352 with GCF Formula

Least Common Multiple of 522,352 with GCF Formula

The formula of LCM is LCM(a1,a2,a3....,an) = ( a1 × a2 × a3 × .... × an) / GCF(a1,a2,a3....,an) x common factors(if more than 2 numbers have common factors).

We need to calculate greatest common factor of 522,352 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(522,352) = 2

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

GCF(522,352) x common factors =2 x 1 = 2

LCM(522,352) = ( 522 × 352 ) / 2

LCM(522,352) = 183744 / 2

LCM(522,352) = 91872


GCF of Fractions Calculation Examples

FAQs on GCF of Fractions of 589/522, 713/352

1. What is the HCF of 589,713?

The HCF of 589,713 is 31

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 589/522, 713/352?

Answer: GCF of Numerators as per given numbers 589/522, 713/352 is

GCF of Numerators i.e. for 589,713 is 31

LCM of denominators i.e. for 522,352 is 91872.

Thus, GCF of Fractions is 31/91872.Finally, GCF of Fractions for 589/522, 713/352 is 31/91872.