Use our free GCF of Fractions Calculator tool to compute the GCF of 284/584, 810/614 i.e 2/179288 easily. The following is the detailed procedure to determine the greatest common factor of fractions 284/584, 810/614.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 284/584,810/614
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 284/584,810/614, numerators are 284,810
Denominators are 584,614
The GCF of 284,810 is 2 .
LCM of 584,614 is 179288.
The greatest common factor of 284/584,810/614 = [GCF of 284,810]/[LCM of 584,614]= 2/179288
Therefore, the GCF of 284/584,810/614 is 2/179288.
To find the highest common factor of 284,810, we have to find the factors of both numbers and list the highest common factor.
The factors of 284 are 1, 2, 4, 71, 142, 284
The factors of 810 are 1, 2, 3, 5, 6, 9, 10, 15, 18, 27, 30, 45, 54, 81, 90, 135, 162, 270, 405, 810
The HCF of 284,810 is 2.
Lets's calculate GCF of 284,810
2 | 284, 810 |
142, 405 |
∴ So the GCF of the given numbers is 2 = 2
Now, list down the factors of 284
:1,2,4,71,142,284
Now, list down the factors of 810
:1,2,3,5,6,9,10,15,18,27,30,45,54,81,90,135,162,270,405,810
Greatest Common Factor
We found the factors 284,810 . The biggest common factor number is the GCF number.
So the greatest common factor 284,810 is 2.
Lets's calculate LCM of 584,614
2 | 584, 614 |
292, 307 |
∴ So the LCM of the given numbers is 2 x 292 x 307 = 179288
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/179288
Therefore, the GCF of Fractions 284/584,810/614 is 2/179288
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 584,614 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(584,614) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(584,614) x common factors =2 x 1 = 2
LCM(584,614) = ( 584 × 614 ) / 2
LCM(584,614) = 358576 / 2
LCM(584,614) = 179288
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 284,810?
The HCF of 284,810 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 284/584, 810/614?
Answer: GCF of Numerators as per given numbers 284/584, 810/614 is
GCF of Numerators i.e. for 284,810 is 2
LCM of denominators i.e. for 584,614 is 179288.
Thus, GCF of Fractions is 2/179288.Finally, GCF of Fractions for 284/584, 810/614 is 2/179288.