Greatest Common Factor of 189/36, 106/45, 229/310

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

GCF of 189/36, 106/45, 229/310

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 189/36,106/45,229/310

Given fractions are 189/36,106/45,229/310

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 189,106,229

Greatest Common Factor of Numerators i.e. GCF of 189,106,229 is 1 .

LCM of Denominators means LCM of 36,45,310 as per the given fractions.

LCM of 36,45,310 is 5580 as it is the smallest common factor for both these numbers.

Lets's calculate GCF of 189,106,229

GCF of Fractions 189/36,106/45,229/310 is 1/5580

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

Greatest Common Factor of 189,106,229 By Matching Biggest Common Factor Method

Greatest Common Factor of 189,106,229 By Matching Biggest Common Factor Method

Factors of 189

List of positive integer factors of 189 that divides 189 without a remainder.

1,3,7,9,21,27,63,189

Factors of 106

List of positive integer factors of 106 that divides 106 without a remainder.

1,2,53,106

Factors of 229

List of positive integer factors of 229 that divides 229 without a remainder.

1,229

Greatest Common Factor

We found the factors 189,106,229 . The biggest common factor number is the GCF number.
So the greatest common factor 189,106,229 is 1.

Lets's calculate LCM of 36,45,310

2 36, 45, 310
3 18, 45, 155
3 6, 15, 155
5 2, 5, 155
2, 1, 31

∴ So the LCM of the given numbers is 2 x 3 x 3 x 5 x 2 x 1 x 31 = 5580

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/5580

Therefore, the GCF of Fractions 189/36,106/45,229/310 is 1/5580

Least Common Multiple of 36,45,310 with GCF Formula

Least Common Multiple of 36,45,310 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 36,45,310 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(36,45,310) = 1

common factors(in case of two or more numbers have common factors) = 90

GCF(36,45,310) x common factors =1 x 90 = 90

LCM(36,45,310) = ( 36 × 45 × 310 ) / 90

LCM(36,45,310) = 502200 / 90

LCM(36,45,310) = 5580


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 189/36, 106/45, 229/310

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 189/36, 106/45, 229/310?

Answer: GCF of Numerators as per given numbers 189/36, 106/45, 229/310 is

GCF of Numerators i.e. for 189,106,229 is 1

LCM of denominators i.e. for 36,45,310 is 5580.

Thus, GCF of Fractions is 1/5580.Finally, GCF of Fractions for 189/36, 106/45, 229/310 is 1/5580.