How to Find GCF of 500/318, 8371/6514?

GCF of 500/318, 8371/6514

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 500/318, 8371/6514 i.e 1/1035726 easily. The following is the detailed procedure to determine the greatest common factor of fractions 500/318, 8371/6514.

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 500/318,8371/6514?

Given fractions are 500/318,8371/6514

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 500/318,8371/6514, numerators are 500,8371

Denominators are 318,6514

The GCF of 500,8371 is 1 .

LCM of 318,6514 is 1035726.

The greatest common factor of 500/318,8371/6514 = [GCF of 500,8371]/[LCM of 318,6514]= 1/1035726

Therefore, the GCF of 500/318,8371/6514 is 1/1035726.

Greatest Common Factor of 500,8371

To find the highest common factor of 500,8371, we have to find the factors of both numbers and list the highest common factor.

The factors of 500 are 1, 2, 4, 5, 10, 20, 25, 50, 100, 125, 250, 500

The factors of 8371 are 1, 11, 761, 8371

The HCF of 500,8371 is 1.

Lets's calculate GCF of 500,8371

Greatest Common Factor (GCF) of 500,8371 By Common Division

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

Greatest Common Factor of 500,8371 By Matching Biggest Common Factor Method

Now, list down the factors of 500

1,2,4,5,10,20,25,50,100,125,250,500

Now, list down the factors of 8371

1,11,761,8371

Greatest Common Factor

We found the factors 500,8371 . The biggest common factor number is the GCF number.
So the greatest common factor 500,8371 is 1.

Lets's calculate LCM of 318,6514

Lowest Common Multiple of 318,6514 using Common Division

2	318, 6514
	159, 3257

∴ So the LCM of the given numbers is 2 x 159 x 3257 = 1035726

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/1035726

Therefore, the GCF of Fractions 500/318,8371/6514 is 1/1035726

Least Common Multiple of 318,6514 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 318,6514 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(318,6514) = 2

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

GCF(318,6514) x common factors =2 x 1 = 2

LCM(318,6514) = ( 318 × 6514 ) / 2

LCM(318,6514) = 2071452 / 2

LCM(318,6514) = 1035726

GCF of Fractions Calculation Examples

Here are some samples of GCF of Fractions calculations.

FAQs on GCF of Fractions of 500/318, 8371/6514

1. What is the HCF of 500,8371?

The HCF of 500,8371 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 500/318, 8371/6514?

Answer: GCF of Numerators as per given numbers 500/318, 8371/6514 is

GCF of Numerators i.e. for 500,8371 is 1

LCM of denominators i.e. for 318,6514 is 1035726.

Thus, GCF of Fractions is 1/1035726.Finally, GCF of Fractions for 500/318, 8371/6514 is 1/1035726.