Greatest Common Factor of 29/23, 38/18, 14/65, 17/14

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

GCF of 29/23, 38/18, 14/65, 17/14

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 29/23,38/18,14/65,17/14

Given fractions are 29/23,38/18,14/65,17/14

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 29,38,14,17

Greatest Common Factor of Numerators i.e. GCF of 29,38,14,17 is 1 .

LCM of Denominators means LCM of 23,18,65,14 as per the given fractions.

LCM of 23,18,65,14 is 188370 as it is the smallest common factor for both these numbers.

Lets's calculate GCF of 29,38,14,17

GCF of Fractions 29/23,38/18,14/65,17/14 is 1/188370

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

Greatest Common Factor of 29,38,14,17 By Matching Biggest Common Factor Method

Greatest Common Factor of 29,38,14,17 By Matching Biggest Common Factor Method

Factors of 29

List of positive integer factors of 29 that divides 29 without a remainder.

1,29

Factors of 38

List of positive integer factors of 38 that divides 38 without a remainder.

1,2,19,38

Factors of 14

List of positive integer factors of 14 that divides 14 without a remainder.

1,2,7,14

Factors of 17

List of positive integer factors of 17 that divides 17 without a remainder.

1,17

Greatest Common Factor

We found the factors 29,38,14,17 . The biggest common factor number is the GCF number.
So the greatest common factor 29,38,14,17 is 1.

Lets's calculate LCM of 23,18,65,14

2 23, 18, 65, 14
23, 9, 65, 7

∴ So the LCM of the given numbers is 2 x 23 x 9 x 65 x 7 = 188370

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/188370

Therefore, the GCF of Fractions 29/23,38/18,14/65,17/14 is 1/188370

Least Common Multiple of 23,18,65,14 with GCF Formula

Least Common Multiple of 23,18,65,14 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 23,18,65,14 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(23,18,65,14) = 1

common factors(in case of two or more numbers have common factors) = 2

GCF(23,18,65,14) x common factors =1 x 2 = 2

LCM(23,18,65,14) = ( 23 × 18 × 65 × 14 ) / 2

LCM(23,18,65,14) = 376740 / 2

LCM(23,18,65,14) = 188370


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 29/23, 38/18, 14/65, 17/14

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 29/23, 38/18, 14/65, 17/14?

Answer: GCF of Numerators as per given numbers 29/23, 38/18, 14/65, 17/14 is

GCF of Numerators i.e. for 29,38,14,17 is 1

LCM of denominators i.e. for 23,18,65,14 is 188370.

Thus, GCF of Fractions is 1/188370.Finally, GCF of Fractions for 29/23, 38/18, 14/65, 17/14 is 1/188370.