Greatest Common Factor of 75/60, 69/18, 39/10, 42/24

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

GCF of 75/60, 69/18, 39/10, 42/24

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 75/60,69/18,39/10,42/24

Given fractions are 75/60,69/18,39/10,42/24

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 75,69,39,42

Greatest Common Factor of Numerators i.e. GCF of 75,69,39,42 is 3 .

LCM of Denominators means LCM of 60,18,10,24 as per the given fractions.

LCM of 60,18,10,24 is 360 as it is the smallest common factor for both these numbers.

Lets's calculate GCF of 75,69,39,42

GCF of Fractions 75/60,69/18,39/10,42/24 is 3/360

3 75, 69, 39, 42
25, 23, 13, 14

∴ So the GCF of the given numbers is 3 = 3

Greatest Common Factor of 75,69,39,42 By Matching Biggest Common Factor Method

Greatest Common Factor of 75,69,39,42 By Matching Biggest Common Factor Method

Factors of 75

List of positive integer factors of 75 that divides 75 without a remainder.

1,3,5,15,25,75

Factors of 69

List of positive integer factors of 69 that divides 69 without a remainder.

1,3,23,69

Factors of 39

List of positive integer factors of 39 that divides 39 without a remainder.

1,3,13,39

Factors of 42

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

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

Greatest Common Factor

We found the factors 75,69,39,42 . The biggest common factor number is the GCF number.
So the greatest common factor 75,69,39,42 is 3.

Lets's calculate LCM of 60,18,10,24

2 60, 18, 10, 24
2 30, 9, 5, 12
3 15, 9, 5, 6
5 5, 3, 5, 2
1, 3, 1, 2

∴ So the LCM of the given numbers is 2 x 2 x 3 x 5 x 1 x 3 x 1 x 2 = 360

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 3/360

Therefore, the GCF of Fractions 75/60,69/18,39/10,42/24 is 3/360

Least Common Multiple of 60,18,10,24 with GCF Formula

Least Common Multiple of 60,18,10,24 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 60,18,10,24 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(60,18,10,24) = 2

common factors(in case of two or more numbers have common factors) = 360

GCF(60,18,10,24) x common factors =2 x 360 = 720

LCM(60,18,10,24) = ( 60 × 18 × 10 × 24 ) / 720

LCM(60,18,10,24) = 259200 / 720

LCM(60,18,10,24) = 360


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 75/60, 69/18, 39/10, 42/24

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 75/60, 69/18, 39/10, 42/24?

Answer: GCF of Numerators as per given numbers 75/60, 69/18, 39/10, 42/24 is

GCF of Numerators i.e. for 75,69,39,42 is 3

LCM of denominators i.e. for 60,18,10,24 is 360.

Thus, GCF of Fractions is 3/360.Finally, GCF of Fractions for 75/60, 69/18, 39/10, 42/24 is 3/360.