Use our free GCF of Fractions Calculator tool to compute the GCF of 816/267, 828/704 i.e 12/187968 easily. The following is the detailed procedure to determine the greatest common factor of fractions 816/267, 828/704.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 816/267,828/704
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 816/267,828/704, numerators are 816,828
Denominators are 267,704
The GCF of 816,828 is 12 .
LCM of 267,704 is 187968.
The greatest common factor of 816/267,828/704 = [GCF of 816,828]/[LCM of 267,704]= 12/187968
Therefore, the GCF of 816/267,828/704 is 12/187968.
To find the highest common factor of 816,828, we have to find the factors of both numbers and list the highest common factor.
The factors of 816 are 1, 2, 3, 4, 6, 8, 12, 16, 17, 24, 34, 48, 51, 68, 102, 136, 204, 272, 408, 816
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 816,828 is 12.
Lets's calculate GCF of 816,828
2 | 816, 828 |
2 | 408, 414 |
3 | 204, 207 |
68, 69 |
∴ So the GCF of the given numbers is 2 x 2 x 3 = 12
Now, list down the factors of 816
:1,2,3,4,6,8,12,16,17,24,34,48,51,68,102,136,204,272,408,816
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 816,828 . The biggest common factor number is the GCF number.
So the greatest common factor 816,828 is 12.
Lets's calculate LCM of 267,704
Given numbers has no common factors except 1. So, there LCM is their product i.e 187968
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 12/187968
Therefore, the GCF of Fractions 816/267,828/704 is 12/187968
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 267,704 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(267,704) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(267,704) x common factors =1 x 1 = 1
LCM(267,704) = ( 267 × 704 ) / 1
LCM(267,704) = 187968 / 1
LCM(267,704) = 187968
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 816,828?
The HCF of 816,828 is 12
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 816/267, 828/704?
Answer: GCF of Numerators as per given numbers 816/267, 828/704 is
GCF of Numerators i.e. for 816,828 is 12
LCM of denominators i.e. for 267,704 is 187968.
Thus, GCF of Fractions is 12/187968.Finally, GCF of Fractions for 816/267, 828/704 is 12/187968.