How to Find GCF of 500/86, 420/671?

GCF of 500/86, 420/671

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 500/86, 420/671 i.e 20/57706 easily. The following is the detailed procedure to determine the greatest common factor of fractions 500/86, 420/671.

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 500/86,420/671?

Given fractions are 500/86,420/671

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 500/86,420/671, numerators are 500,420

Denominators are 86,671

The GCF of 500,420 is 20 .

LCM of 86,671 is 57706.

The greatest common factor of 500/86,420/671 = [GCF of 500,420]/[LCM of 86,671]= 20/57706

Therefore, the GCF of 500/86,420/671 is 20/57706.

Greatest Common Factor of 500,420

To find the highest common factor of 500,420, we have to find the factors of both numbers and list the highest common factor.

The factors of 500 are 1, 2, 4, 5, 10, 20, 25, 50, 100, 125, 250, 500

The factors of 420 are 1, 2, 3, 4, 5, 6, 7, 10, 12, 14, 15, 20, 21, 28, 30, 35, 42, 60, 70, 84, 105, 140, 210, 420

The HCF of 500,420 is 20.

Lets's calculate GCF of 500,420

Greatest Common Factor (GCF) of 500,420 By Common Division

2	500, 420
2	250, 210
5	125, 105
	25, 21

∴ So the GCF of the given numbers is 2 x 2 x 5 = 20

Greatest Common Factor of 500,420 By Matching Biggest Common Factor Method

Now, list down the factors of 500

1,2,4,5,10,20,25,50,100,125,250,500

Now, list down the factors of 420

1,2,3,4,5,6,7,10,12,14,15,20,21,28,30,35,42,60,70,84,105,140,210,420

Greatest Common Factor

We found the factors 500,420 . The biggest common factor number is the GCF number.
So the greatest common factor 500,420 is 20.

Lets's calculate LCM of 86,671

Lowest Common Multiple of 86,671 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 57706

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 20/57706

Therefore, the GCF of Fractions 500/86,420/671 is 20/57706

Least Common Multiple of 86,671 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 86,671 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(86,671) = 1

common factors(in case of two or more numbers have common factors) = 1

GCF(86,671) x common factors =1 x 1 = 1

LCM(86,671) = ( 86 × 671 ) / 1

LCM(86,671) = 57706 / 1

LCM(86,671) = 57706

GCF of Fractions Calculation Examples

Here are some samples of GCF of Fractions calculations.

FAQs on GCF of Fractions of 500/86, 420/671

1. What is the HCF of 500,420?

The HCF of 500,420 is 20

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 500/86, 420/671?

Answer: GCF of Numerators as per given numbers 500/86, 420/671 is

GCF of Numerators i.e. for 500,420 is 20

LCM of denominators i.e. for 86,671 is 57706.

Thus, GCF of Fractions is 20/57706.Finally, GCF of Fractions for 500/86, 420/671 is 20/57706.