Greatest Common Factor of 42/30, 84/13, 289/18

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

GCF of 42/30, 84/13, 289/18

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 42/30,84/13,289/18

Given fractions are 42/30,84/13,289/18

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 42,84,289

Greatest Common Factor of Numerators i.e. GCF of 42,84,289 is 1 .

LCM of Denominators means LCM of 30,13,18 as per the given fractions.

LCM of 30,13,18 is 1170 as it is the smallest common factor for both these numbers.

Lets's calculate GCF of 42,84,289

GCF of Fractions 42/30,84/13,289/18 is 1/1170

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

Greatest Common Factor of 42,84,289 By Matching Biggest Common Factor Method

Greatest Common Factor of 42,84,289 By Matching Biggest Common Factor Method

Factors of 42

List of positive integer factors of 42 that divides 42 without a remainder.

1,2,3,6,7,14,21,42

Factors of 84

List of positive integer factors of 84 that divides 84 without a remainder.

1,2,3,4,6,7,12,14,21,28,42,84

Factors of 289

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

1,17,289

Greatest Common Factor

We found the factors 42,84,289 . The biggest common factor number is the GCF number.
So the greatest common factor 42,84,289 is 1.

Lets's calculate LCM of 30,13,18

2 30, 13, 18
3 15, 13, 9
5, 13, 3

∴ So the LCM of the given numbers is 2 x 3 x 5 x 13 x 3 = 1170

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/1170

Therefore, the GCF of Fractions 42/30,84/13,289/18 is 1/1170

Least Common Multiple of 30,13,18 with GCF Formula

Least Common Multiple of 30,13,18 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 30,13,18 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(30,13,18) = 1

common factors(in case of two or more numbers have common factors) = 6

GCF(30,13,18) x common factors =1 x 6 = 6

LCM(30,13,18) = ( 30 × 13 × 18 ) / 6

LCM(30,13,18) = 7020 / 6

LCM(30,13,18) = 1170


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 42/30, 84/13, 289/18

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 42/30, 84/13, 289/18?

Answer: GCF of Numerators as per given numbers 42/30, 84/13, 289/18 is

GCF of Numerators i.e. for 42,84,289 is 1

LCM of denominators i.e. for 30,13,18 is 1170.

Thus, GCF of Fractions is 1/1170.Finally, GCF of Fractions for 42/30, 84/13, 289/18 is 1/1170.