Use our free GCF of Fractions Calculator tool to compute the GCF of 855/72, 816/824 i.e 3/7416 easily. The following is the detailed procedure to determine the greatest common factor of fractions 855/72, 816/824.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 855/72,816/824
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 855/72,816/824, numerators are 855,816
Denominators are 72,824
The GCF of 855,816 is 3 .
LCM of 72,824 is 7416.
The greatest common factor of 855/72,816/824 = [GCF of 855,816]/[LCM of 72,824]= 3/7416
Therefore, the GCF of 855/72,816/824 is 3/7416.
To find the highest common factor of 855,816, we have to find the factors of both numbers and list the highest common factor.
The factors of 855 are 1, 3, 5, 9, 15, 19, 45, 57, 95, 171, 285, 855
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 HCF of 855,816 is 3.
Lets's calculate GCF of 855,816
3 | 855, 816 |
285, 272 |
∴ So the GCF of the given numbers is 3 = 3
Now, list down the factors of 855
:1,3,5,9,15,19,45,57,95,171,285,855
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
Greatest Common Factor
We found the factors 855,816 . The biggest common factor number is the GCF number.
So the greatest common factor 855,816 is 3.
Lets's calculate LCM of 72,824
2 | 72, 824 |
2 | 36, 412 |
2 | 18, 206 |
9, 103 |
∴ So the LCM of the given numbers is 2 x 2 x 2 x 9 x 103 = 7416
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 3/7416
Therefore, the GCF of Fractions 855/72,816/824 is 3/7416
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 72,824 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(72,824) = 8
common factors(in case of two or more numbers have common factors) = 1
GCF(72,824) x common factors =8 x 1 = 8
LCM(72,824) = ( 72 × 824 ) / 8
LCM(72,824) = 59328 / 8
LCM(72,824) = 7416
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 855,816?
The HCF of 855,816 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 855/72, 816/824?
Answer: GCF of Numerators as per given numbers 855/72, 816/824 is
GCF of Numerators i.e. for 855,816 is 3
LCM of denominators i.e. for 72,824 is 7416.
Thus, GCF of Fractions is 3/7416.Finally, GCF of Fractions for 855/72, 816/824 is 3/7416.