Greatest Common Factor of 728/84, 213/17, 365/80

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

GCF of 728/84, 213/17, 365/80

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 728/84,213/17,365/80

Given fractions are 728/84,213/17,365/80

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 728,213,365

Greatest Common Factor of Numerators i.e. GCF of 728,213,365 is 1 .

LCM of Denominators means LCM of 84,17,80 as per the given fractions.

LCM of 84,17,80 is 28560 as it is the smallest common factor for both these numbers.

Lets's calculate GCF of 728,213,365

GCF of Fractions 728/84,213/17,365/80 is 1/28560

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

Greatest Common Factor of 728,213,365 By Matching Biggest Common Factor Method

Greatest Common Factor of 728,213,365 By Matching Biggest Common Factor Method

Factors of 728

List of positive integer factors of 728 that divides 728 without a remainder.

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

Factors of 213

List of positive integer factors of 213 that divides 213 without a remainder.

1,3,71,213

Factors of 365

List of positive integer factors of 365 that divides 365 without a remainder.

1,5,73,365

Greatest Common Factor

We found the factors 728,213,365 . The biggest common factor number is the GCF number.
So the greatest common factor 728,213,365 is 1.

Lets's calculate LCM of 84,17,80

2 84, 17, 80
2 42, 17, 40
21, 17, 20

∴ So the LCM of the given numbers is 2 x 2 x 21 x 17 x 20 = 28560

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/28560

Therefore, the GCF of Fractions 728/84,213/17,365/80 is 1/28560

Least Common Multiple of 84,17,80 with GCF Formula

Least Common Multiple of 84,17,80 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 84,17,80 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(84,17,80) = 1

common factors(in case of two or more numbers have common factors) = 4

GCF(84,17,80) x common factors =1 x 4 = 4

LCM(84,17,80) = ( 84 × 17 × 80 ) / 4

LCM(84,17,80) = 114240 / 4

LCM(84,17,80) = 28560


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 728/84, 213/17, 365/80

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 728/84, 213/17, 365/80?

Answer: GCF of Numerators as per given numbers 728/84, 213/17, 365/80 is

GCF of Numerators i.e. for 728,213,365 is 1

LCM of denominators i.e. for 84,17,80 is 28560.

Thus, GCF of Fractions is 1/28560.Finally, GCF of Fractions for 728/84, 213/17, 365/80 is 1/28560.