GCF of 8121/378, 2000/6564
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 8121/378, 2000/6564 i.e 1/413532 easily. The following is the detailed procedure to determine the greatest common factor of fractions 8121/378, 2000/6564.
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 8121/378,2000/6564?
Given fractions are 8121/378,2000/6564
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 8121/378,2000/6564, numerators are 8121,2000
Denominators are 378,6564
The GCF of 8121,2000 is 1 .
LCM of 378,6564 is 413532.
The greatest common factor of 8121/378,2000/6564 = [GCF of 8121,2000]/[LCM of 378,6564]= 1/413532
Therefore, the GCF of 8121/378,2000/6564 is 1/413532.
To find the highest common factor of 8121,2000, we have to find the factors of both numbers and list the highest common factor.
The factors of 8121 are 1, 3, 2707, 8121
The factors of 2000 are 1, 2, 4, 5, 8, 10, 16, 20, 25, 40, 50, 80, 100, 125, 200, 250, 400, 500, 1000, 2000
The HCF of 8121,2000 is 1.
Lets's calculate GCF of 8121,2000
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 8121,2000 By Matching Biggest Common Factor Method
Now, list down the factors of 8121
:1,3,2707,8121
Now, list down the factors of 2000
:1,2,4,5,8,10,16,20,25,40,50,80,100,125,200,250,400,500,1000,2000
Greatest Common Factor
We found the factors 8121,2000 . The biggest common factor number is the GCF number.
So the greatest common factor 8121,2000 is 1.
Lets's calculate LCM of 378,6564
| 2 | 378, 6564 |
| 3 | 189, 3282 |
| 63, 1094 |
∴ So the LCM of the given numbers is 2 x 3 x 63 x 1094 = 413532
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/413532
Therefore, the GCF of Fractions 8121/378,2000/6564 is 1/413532
Least Common Multiple of 378,6564 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 378,6564 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(378,6564) = 6
common factors(in case of two or more numbers have common factors) = 1
GCF(378,6564) x common factors =6 x 1 = 6
LCM(378,6564) = ( 378 × 6564 ) / 6
LCM(378,6564) = 2481192 / 6
LCM(378,6564) = 413532
GCF of Fractions Calculation Examples
Here are some samples of GCF of Fractions calculations.
FAQs on GCF of Fractions of 8121/378, 2000/6564
1. What is the HCF of 8121,2000?
The HCF of 8121,2000 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 8121/378, 2000/6564?
Answer: GCF of Numerators as per given numbers 8121/378, 2000/6564 is
GCF of Numerators i.e. for 8121,2000 is 1
LCM of denominators i.e. for 378,6564 is 413532.
Thus, GCF of Fractions is 1/413532.Finally, GCF of Fractions for 8121/378, 2000/6564 is 1/413532.