Greatest Common Factor of 289/189, 400/140

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

GCF of 289/189, 400/140

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 289/189,400/140

Given fractions are 289/189,400/140

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 289,400

Greatest Common Factor of Numerators i.e. GCF of 289,400 is 1 .

LCM of Denominators means LCM of 189,140 as per the given fractions.

LCM of 189,140 is 3780 as it is the smallest common factor for both these numbers.

Lets's calculate GCF of 289,400

GCF of Fractions 289/189,400/140 is 1/3780

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

Greatest Common Factor of 289,400 By Matching Biggest Common Factor Method

Greatest Common Factor of 289,400 By Matching Biggest Common Factor Method

Factors of 289

List of positive integer factors of 289 that divides 289 without a remainder.

1,17,289

Factors of 400

List of positive integer factors of 400 that divides 400 without a remainder.

1,2,4,5,8,10,16,20,25,40,50,80,100,200,400

Greatest Common Factor

We found the factors 289,400 . The biggest common factor number is the GCF number.
So the greatest common factor 289,400 is 1.

Lets's calculate LCM of 189,140

7 189, 140
27, 20

∴ So the LCM of the given numbers is 7 x 27 x 20 = 3780

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/3780

Therefore, the GCF of Fractions 289/189,400/140 is 1/3780

Least Common Multiple of 189,140 with GCF Formula

Least Common Multiple of 189,140 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 189,140 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(189,140) = 7

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

GCF(189,140) x common factors =7 x 1 = 7

LCM(189,140) = ( 189 × 140 ) / 7

LCM(189,140) = 26460 / 7

LCM(189,140) = 3780


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 289/189, 400/140

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 289/189, 400/140?

Answer: GCF of Numerators as per given numbers 289/189, 400/140 is

GCF of Numerators i.e. for 289,400 is 1

LCM of denominators i.e. for 189,140 is 3780.

Thus, GCF of Fractions is 1/3780.Finally, GCF of Fractions for 289/189, 400/140 is 1/3780.