How to Find GCF of 20/506, 31/407, 360/142?

GCF of 20/506, 31/407, 360/142

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 20/506, 31/407, 360/142 i.e 1/1329262 easily. The following is the detailed procedure to determine the greatest common factor of fractions 20/506, 31/407, 360/142.

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 20/506,31/407,360/142?

Given fractions are 20/506,31/407,360/142

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 20/506,31/407,360/142, numerators are 20,31,360

Denominators are 506,407,142

The GCF of 20,31,360 is 1 .

LCM of 506,407,142 is 1329262.

The greatest common factor of 20/506,31/407,360/142 = [GCF of 20,31,360]/[LCM of 506,407,142]= 1/1329262

Therefore, the GCF of 20/506,31/407,360/142 is 1/1329262.

Greatest Common Factor of 20,31,360

To find the highest common factor of 20,31,360, we have to find the factors of both numbers and list the highest common factor.

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

The factors of 31 are 1, 31

The factors of 360 are 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, 24, 30, 36, 40, 45, 60, 72, 90, 120, 180, 360

The HCF of 20,31,360 is 1.

Lets's calculate GCF of 20,31,360

Greatest Common Factor (GCF) of 20,31,360 By Common Division

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

Greatest Common Factor of 20,31,360 By Matching Biggest Common Factor Method

Now, list down the factors of 20

1,2,4,5,10,20

Now, list down the factors of 31

1,31

Now, list down the factors of 360

1,2,3,4,5,6,8,9,10,12,15,18,20,24,30,36,40,45,60,72,90,120,180,360

Greatest Common Factor

We found the factors 20,31,360 . The biggest common factor number is the GCF number.
So the greatest common factor 20,31,360 is 1.

Lets's calculate LCM of 506,407,142

Lowest Common Multiple of 506,407,142 using Common Division

2	506, 407, 142
11	253, 407, 71
	23, 37, 71

∴ So the LCM of the given numbers is 2 x 11 x 23 x 37 x 71 = 1329262

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/1329262

Therefore, the GCF of Fractions 20/506,31/407,360/142 is 1/1329262

Least Common Multiple of 506,407,142 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 506,407,142 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(506,407,142) = 1

common factors(in case of two or more numbers have common factors) = 22

GCF(506,407,142) x common factors =1 x 22 = 22

LCM(506,407,142) = ( 506 × 407 × 142 ) / 22

LCM(506,407,142) = 29243764 / 22

LCM(506,407,142) = 1329262

GCF of Fractions Calculation Examples

Here are some samples of GCF of Fractions calculations.

FAQs on GCF of Fractions of 20/506, 31/407, 360/142

1. What is the HCF of 20,31,360?

The HCF of 20,31,360 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 20/506, 31/407, 360/142?

Answer: GCF of Numerators as per given numbers 20/506, 31/407, 360/142 is

GCF of Numerators i.e. for 20,31,360 is 1

LCM of denominators i.e. for 506,407,142 is 1329262.

Thus, GCF of Fractions is 1/1329262.Finally, GCF of Fractions for 20/506, 31/407, 360/142 is 1/1329262.