Use our free GCF of Fractions Calculator tool to compute the GCF of 231/510, 828/850 i.e 3/2550 easily. The following is the detailed procedure to determine the greatest common factor of fractions 231/510, 828/850.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 231/510,828/850
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 231/510,828/850, numerators are 231,828
Denominators are 510,850
The GCF of 231,828 is 3 .
LCM of 510,850 is 2550.
The greatest common factor of 231/510,828/850 = [GCF of 231,828]/[LCM of 510,850]= 3/2550
Therefore, the GCF of 231/510,828/850 is 3/2550.
To find the highest common factor of 231,828, we have to find the factors of both numbers and list the highest common factor.
The factors of 231 are 1, 3, 7, 11, 21, 33, 77, 231
The factors of 828 are 1, 2, 3, 4, 6, 9, 12, 18, 23, 36, 46, 69, 92, 138, 207, 276, 414, 828
The HCF of 231,828 is 3.
Lets's calculate GCF of 231,828
3 | 231, 828 |
77, 276 |
∴ So the GCF of the given numbers is 3 = 3
Now, list down the factors of 231
:1,3,7,11,21,33,77,231
Now, list down the factors of 828
:1,2,3,4,6,9,12,18,23,36,46,69,92,138,207,276,414,828
Greatest Common Factor
We found the factors 231,828 . The biggest common factor number is the GCF number.
So the greatest common factor 231,828 is 3.
Lets's calculate LCM of 510,850
2 | 510, 850 |
5 | 255, 425 |
17 | 51, 85 |
3, 5 |
∴ So the LCM of the given numbers is 2 x 5 x 17 x 3 x 5 = 2550
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 3/2550
Therefore, the GCF of Fractions 231/510,828/850 is 3/2550
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 510,850 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(510,850) = 170
common factors(in case of two or more numbers have common factors) = 1
GCF(510,850) x common factors =170 x 1 = 170
LCM(510,850) = ( 510 × 850 ) / 170
LCM(510,850) = 433500 / 170
LCM(510,850) = 2550
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 231,828?
The HCF of 231,828 is 3
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 231/510, 828/850?
Answer: GCF of Numerators as per given numbers 231/510, 828/850 is
GCF of Numerators i.e. for 231,828 is 3
LCM of denominators i.e. for 510,850 is 2550.
Thus, GCF of Fractions is 3/2550.Finally, GCF of Fractions for 231/510, 828/850 is 3/2550.