How to Find GCF of 59/31, 46/14, 20/86, 27/82?

GCF of 59/31, 46/14, 20/86, 27/82

Created By : Veerendra
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023

Use our free GCF of Fractions Calculator tool to compute the GCF of 59/31, 46/14, 20/86, 27/82 i.e 1/765142 easily. The following is the detailed procedure to determine the greatest common factor of fractions 59/31, 46/14, 20/86, 27/82.

Enter two or more fractions separated by "commas"

Ex: 2/3, 5/7 or 3/5, 5/9, 7/3

What is the GCF of 59/31,46/14,20/86,27/82?

Given fractions are 59/31,46/14,20/86,27/82

To find the GCF of fractions, we have to find the GCF of numerator numbers and LCM of denominator numbers. Its formula is given by

GCF of Fraction = Greatest Common Factor of Numerator/Least Common Multiple of Denominators

In the fractions 59/31,46/14,20/86,27/82, numerators are 59,46,20,27

Denominators are 31,14,86,82

The GCF of 59,46,20,27 is 1 .

LCM of 31,14,86,82 is 765142.

The greatest common factor of 59/31,46/14,20/86,27/82 = [GCF of 59,46,20,27]/[LCM of 31,14,86,82]= 1/765142

Therefore, the GCF of 59/31,46/14,20/86,27/82 is 1/765142.

Greatest Common Factor of 59,46,20,27

To find the highest common factor of 59,46,20,27, we have to find the factors of both numbers and list the highest common factor.

The factors of 59 are 1, 59

The factors of 46 are 1, 2, 23, 46

The factors of 20 are 1, 2, 4, 5, 10, 20

The factors of 27 are 1, 3, 9, 27

The HCF of 59,46,20,27 is 1.

Lets's calculate GCF of 59,46,20,27

Greatest Common Factor (GCF) of 59,46,20,27 By Common Division

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

Greatest Common Factor of 59,46,20,27 By Matching Biggest Common Factor Method

Now, list down the factors of 59

1,59

Now, list down the factors of 46

1,2,23,46

Now, list down the factors of 20

1,2,4,5,10,20

Now, list down the factors of 27

1,3,9,27

Greatest Common Factor

We found the factors 59,46,20,27 . The biggest common factor number is the GCF number.
So the greatest common factor 59,46,20,27 is 1.

Lets's calculate LCM of 31,14,86,82

Lowest Common Multiple of 31,14,86,82 using Common Division

2	31, 14, 86, 82
	31, 7, 43, 41

∴ So the LCM of the given numbers is 2 x 31 x 7 x 43 x 41 = 765142

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/765142

Therefore, the GCF of Fractions 59/31,46/14,20/86,27/82 is 1/765142

Least Common Multiple of 31,14,86,82 with GCF Formula

The formula of LCM is LCM(a₁,a₂,a₃....,a_n) = ( a₁ × a₂ × a₃ × .... × a_n) / GCF(a₁,a₂,a₃....,a_n) x common factors(if more than 2 numbers have common factors).

We need to calculate greatest common factor of 31,14,86,82 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(31,14,86,82) = 1

common factors(in case of two or more numbers have common factors) = 4

GCF(31,14,86,82) x common factors =1 x 4 = 4

LCM(31,14,86,82) = ( 31 × 14 × 86 × 82 ) / 4

LCM(31,14,86,82) = 3060568 / 4

LCM(31,14,86,82) = 765142

GCF of Fractions Calculation Examples

Here are some samples of GCF of Fractions calculations.

FAQs on GCF of Fractions of 59/31, 46/14, 20/86, 27/82

1. What is the HCF of 59,46,20,27?

The HCF of 59,46,20,27 is 1

2. What is the GCF of a fraction?

The GCF of a fraction is defined as the greatest fraction that divides exactly into 2 or more fractions.

3. 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.

4. What is the GCF of Fractions for 59/31, 46/14, 20/86, 27/82?

Answer: GCF of Numerators as per given numbers 59/31, 46/14, 20/86, 27/82 is

GCF of Numerators i.e. for 59,46,20,27 is 1

LCM of denominators i.e. for 31,14,86,82 is 765142.

Thus, GCF of Fractions is 1/765142.Finally, GCF of Fractions for 59/31, 46/14, 20/86, 27/82 is 1/765142.