Greatest Common Factor of 36/30, 70/65, 85/84, 31/723

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

GCF of 36/30, 70/65, 85/84, 31/723

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 36/30,70/65,85/84,31/723

Given fractions are 36/30,70/65,85/84,31/723

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 36,70,85,31

Greatest Common Factor of Numerators i.e. GCF of 36,70,85,31 is 1 .

LCM of Denominators means LCM of 30,65,84,723 as per the given fractions.

LCM of 30,65,84,723 is 1315860 as it is the smallest common factor for both these numbers.

Lets's calculate GCF of 36,70,85,31

GCF of Fractions 36/30,70/65,85/84,31/723 is 1/1315860

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

Greatest Common Factor of 36,70,85,31 By Matching Biggest Common Factor Method

Greatest Common Factor of 36,70,85,31 By Matching Biggest Common Factor Method

Factors of 36

List of positive integer factors of 36 that divides 36 without a remainder.

1,2,3,4,6,9,12,18,36

Factors of 70

List of positive integer factors of 70 that divides 70 without a remainder.

1,2,5,7,10,14,35,70

Factors of 85

List of positive integer factors of 85 that divides 85 without a remainder.

1,5,17,85

Factors of 31

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

1,31

Greatest Common Factor

We found the factors 36,70,85,31 . The biggest common factor number is the GCF number.
So the greatest common factor 36,70,85,31 is 1.

Lets's calculate LCM of 30,65,84,723

2 30, 65, 84, 723
3 15, 65, 42, 723
5 5, 65, 14, 241
1, 13, 14, 241

∴ So the LCM of the given numbers is 2 x 3 x 5 x 1 x 13 x 14 x 241 = 1315860

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/1315860

Therefore, the GCF of Fractions 36/30,70/65,85/84,31/723 is 1/1315860

Least Common Multiple of 30,65,84,723 with GCF Formula

Least Common Multiple of 30,65,84,723 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 30,65,84,723 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(30,65,84,723) = 1

common factors(in case of two or more numbers have common factors) = 90

GCF(30,65,84,723) x common factors =1 x 90 = 90

LCM(30,65,84,723) = ( 30 × 65 × 84 × 723 ) / 90

LCM(30,65,84,723) = 118427400 / 90

LCM(30,65,84,723) = 1315860


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 36/30, 70/65, 85/84, 31/723

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 36/30, 70/65, 85/84, 31/723?

Answer: GCF of Numerators as per given numbers 36/30, 70/65, 85/84, 31/723 is

GCF of Numerators i.e. for 36,70,85,31 is 1

LCM of denominators i.e. for 30,65,84,723 is 1315860.

Thus, GCF of Fractions is 1/1315860.Finally, GCF of Fractions for 36/30, 70/65, 85/84, 31/723 is 1/1315860.