Greatest Common Factor of 217/314, 8000/321

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

GCF of 217/314, 8000/321

Enter two or more fractions separated by "commas"

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

GCF of:

Greatest Common Factor of 217/314,8000/321

Given fractions are 217/314,8000/321

Formula to find GCF of Fractions is

GCF = GCF of Numerators/LCM of Denominators

As per the formula GCF of Fractions let’s split into two parts and find the GCF of Numerators and LCM of Denominators

In the given fractions GCF of Numerators means GCF of 217,8000

Greatest Common Factor of Numerators i.e. GCF of 217,8000 is 1 .

LCM of Denominators means LCM of 314,321 as per the given fractions.

LCM of 314,321 is 100794 as it is the smallest common factor for both these numbers.

Lets's calculate GCF of 217,8000

GCF of Fractions 217/314,8000/321 is 1/100794

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

Greatest Common Factor of 217,8000 By Matching Biggest Common Factor Method

Greatest Common Factor of 217,8000 By Matching Biggest Common Factor Method

Factors of 217

List of positive integer factors of 217 that divides 217 without a remainder.

1,7,31,217

Factors of 8000

List of positive integer factors of 8000 that divides 8000 without a remainder.

1,2,4,5,8,10,16,20,25,32,40,50,64,80,100,125,160,200,250,320,400,500,800,1000,1600,2000,4000,8000

Greatest Common Factor

We found the factors 217,8000 . The biggest common factor number is the GCF number.
So the greatest common factor 217,8000 is 1.

Lets's calculate LCM of 314,321

Given numbers has no common factors except 1. So, there LCM is their product i.e 100794

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/100794

Therefore, the GCF of Fractions 217/314,8000/321 is 1/100794

Least Common Multiple of 314,321 with GCF Formula

Least Common Multiple of 314,321 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 314,321 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(314,321) = 1

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

GCF(314,321) x common factors =1 x 1 = 1

LCM(314,321) = ( 314 × 321 ) / 1

LCM(314,321) = 100794 / 1

LCM(314,321) = 100794


GCF of Fractions Calculation Examples

Here are some samples of GCF of Fractions calculations.

GCF of Fractions Calculation Examples

Here are some samples of GCF of Fractions calculations.

Frequently Asked Questions on Fractional GCF of 217/314, 8000/321

1. 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.

2. What is the GCF of Fractions for 217/314, 8000/321?

Answer: GCF of Numerators as per given numbers 217/314, 8000/321 is

GCF of Numerators i.e. for 217,8000 is 1

LCM of denominators i.e. for 314,321 is 100794.

Thus, GCF of Fractions is 1/100794.Finally, GCF of Fractions for 217/314, 8000/321 is 1/100794.