Greatest Common Factor of 114/23, 288/180

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

GCF of 114/23, 288/180

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 114/23,288/180

Given fractions are 114/23,288/180

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 114,288

Greatest Common Factor of Numerators i.e. GCF of 114,288 is 6 .

LCM of Denominators means LCM of 23,180 as per the given fractions.

LCM of 23,180 is 4140 as it is the smallest common factor for both these numbers.

Lets's calculate GCF of 114,288

GCF of Fractions 114/23,288/180 is 6/4140

2 114, 288
3 57, 144
19, 48

∴ So the GCF of the given numbers is 2 x 3 = 6

Greatest Common Factor of 114,288 By Matching Biggest Common Factor Method

Greatest Common Factor of 114,288 By Matching Biggest Common Factor Method

Factors of 114

List of positive integer factors of 114 that divides 114 without a remainder.

1,2,3,6,19,38,57,114

Factors of 288

List of positive integer factors of 288 that divides 288 without a remainder.

1,2,3,4,6,8,9,12,16,18,24,32,36,48,72,96,144,288

Greatest Common Factor

We found the factors 114,288 . The biggest common factor number is the GCF number.
So the greatest common factor 114,288 is 6.

Lets's calculate LCM of 23,180

Given numbers has no common factors except 1. So, there LCM is their product i.e 4140

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 6/4140

Therefore, the GCF of Fractions 114/23,288/180 is 6/4140

Least Common Multiple of 23,180 with GCF Formula

Least Common Multiple of 23,180 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 23,180 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(23,180) = 1

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

GCF(23,180) x common factors =1 x 1 = 1

LCM(23,180) = ( 23 × 180 ) / 1

LCM(23,180) = 4140 / 1

LCM(23,180) = 4140


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 114/23, 288/180

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 114/23, 288/180?

Answer: GCF of Numerators as per given numbers 114/23, 288/180 is

GCF of Numerators i.e. for 114,288 is 6

LCM of denominators i.e. for 23,180 is 4140.

Thus, GCF of Fractions is 6/4140.Finally, GCF of Fractions for 114/23, 288/180 is 6/4140.