Greatest Common Factor of 40/36, 31/60, 65/30, 75/12

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

GCF of 40/36, 31/60, 65/30, 75/12

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 40/36,31/60,65/30,75/12

Given fractions are 40/36,31/60,65/30,75/12

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 40,31,65,75

Greatest Common Factor of Numerators i.e. GCF of 40,31,65,75 is 1 .

LCM of Denominators means LCM of 36,60,30,12 as per the given fractions.

LCM of 36,60,30,12 is 180 as it is the smallest common factor for both these numbers.

Lets's calculate GCF of 40,31,65,75

GCF of Fractions 40/36,31/60,65/30,75/12 is 1/180

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

Greatest Common Factor of 40,31,65,75 By Matching Biggest Common Factor Method

Greatest Common Factor of 40,31,65,75 By Matching Biggest Common Factor Method

Factors of 40

List of positive integer factors of 40 that divides 40 without a remainder.

1,2,4,5,8,10,20,40

Factors of 31

List of positive integer factors of 31 that divides 31 without a remainder.

1,31

Factors of 65

List of positive integer factors of 65 that divides 65 without a remainder.

1,5,13,65

Factors of 75

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

1,3,5,15,25,75

Greatest Common Factor

We found the factors 40,31,65,75 . The biggest common factor number is the GCF number.
So the greatest common factor 40,31,65,75 is 1.

Lets's calculate LCM of 36,60,30,12

2 36, 60, 30, 12
2 18, 30, 15, 6
3 9, 15, 15, 3
5 1, 5, 5, 3
1, 1, 1, 3

∴ So the LCM of the given numbers is 2 x 2 x 3 x 5 x 1 x 1 x 1 x 3 = 180

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/180

Therefore, the GCF of Fractions 40/36,31/60,65/30,75/12 is 1/180

Least Common Multiple of 36,60,30,12 with GCF Formula

Least Common Multiple of 36,60,30,12 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 36,60,30,12 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(36,60,30,12) = 6

common factors(in case of two or more numbers have common factors) = 720

GCF(36,60,30,12) x common factors =6 x 720 = 4320

LCM(36,60,30,12) = ( 36 × 60 × 30 × 12 ) / 4320

LCM(36,60,30,12) = 777600 / 4320

LCM(36,60,30,12) = 180


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 40/36, 31/60, 65/30, 75/12

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 40/36, 31/60, 65/30, 75/12?

Answer: GCF of Numerators as per given numbers 40/36, 31/60, 65/30, 75/12 is

GCF of Numerators i.e. for 40,31,65,75 is 1

LCM of denominators i.e. for 36,60,30,12 is 180.

Thus, GCF of Fractions is 1/180.Finally, GCF of Fractions for 40/36, 31/60, 65/30, 75/12 is 1/180.