GCF of 1614/566, 8000/6412
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 1614/566, 8000/6412 i.e 2/1814596 easily. The following is the detailed procedure to determine the greatest common factor of fractions 1614/566, 8000/6412.
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 1614/566,8000/6412?
Given fractions are 1614/566,8000/6412
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 1614/566,8000/6412, numerators are 1614,8000
Denominators are 566,6412
The GCF of 1614,8000 is 2 .
LCM of 566,6412 is 1814596.
The greatest common factor of 1614/566,8000/6412 = [GCF of 1614,8000]/[LCM of 566,6412]= 2/1814596
Therefore, the GCF of 1614/566,8000/6412 is 2/1814596.
To find the highest common factor of 1614,8000, we have to find the factors of both numbers and list the highest common factor.
The factors of 1614 are 1, 2, 3, 6, 269, 538, 807, 1614
The factors of 8000 are 1, 2, 4, 5, 8, 10, 16, 20, 25, 32, 40, 50, 64, 80, 100, 125, 160, 200, 250, 320, 400, 500, 800, 1000, 1600, 2000, 4000, 8000
The HCF of 1614,8000 is 2.
Lets's calculate GCF of 1614,8000
| 2 | 1614, 8000 |
| 807, 4000 |
∴ So the GCF of the given numbers is 2 = 2
Greatest Common Factor of 1614,8000 By Matching Biggest Common Factor Method
Now, list down the factors of 1614
:1,2,3,6,269,538,807,1614
Now, list down the factors of 8000
:1,2,4,5,8,10,16,20,25,32,40,50,64,80,100,125,160,200,250,320,400,500,800,1000,1600,2000,4000,8000
Greatest Common Factor
We found the factors 1614,8000 . The biggest common factor number is the GCF number.
So the greatest common factor 1614,8000 is 2.
Lets's calculate LCM of 566,6412
| 2 | 566, 6412 |
| 283, 3206 |
∴ So the LCM of the given numbers is 2 x 283 x 3206 = 1814596
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/1814596
Therefore, the GCF of Fractions 1614/566,8000/6412 is 2/1814596
Least Common Multiple of 566,6412 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 566,6412 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(566,6412) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(566,6412) x common factors =2 x 1 = 2
LCM(566,6412) = ( 566 × 6412 ) / 2
LCM(566,6412) = 3629192 / 2
LCM(566,6412) = 1814596
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FAQs on GCF of Fractions of 1614/566, 8000/6412
1. What is the HCF of 1614,8000?
The HCF of 1614,8000 is 2
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 1614/566, 8000/6412?
Answer: GCF of Numerators as per given numbers 1614/566, 8000/6412 is
GCF of Numerators i.e. for 1614,8000 is 2
LCM of denominators i.e. for 566,6412 is 1814596.
Thus, GCF of Fractions is 2/1814596.Finally, GCF of Fractions for 1614/566, 8000/6412 is 2/1814596.