Use our free GCF of Fractions Calculator tool to compute the GCF of 165/405, 7821/8135 i.e 33/658935 easily. The following is the detailed procedure to determine the greatest common factor of fractions 165/405, 7821/8135.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 165/405,7821/8135
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 165/405,7821/8135, numerators are 165,7821
Denominators are 405,8135
The GCF of 165,7821 is 33 .
LCM of 405,8135 is 658935.
The greatest common factor of 165/405,7821/8135 = [GCF of 165,7821]/[LCM of 405,8135]= 33/658935
Therefore, the GCF of 165/405,7821/8135 is 33/658935.
To find the highest common factor of 165,7821, we have to find the factors of both numbers and list the highest common factor.
The factors of 165 are 1, 3, 5, 11, 15, 33, 55, 165
The factors of 7821 are 1, 3, 9, 11, 33, 79, 99, 237, 711, 869, 2607, 7821
The HCF of 165,7821 is 33.
Lets's calculate GCF of 165,7821
3 | 165, 7821 |
11 | 55, 2607 |
5, 237 |
∴ So the GCF of the given numbers is 3 x 11 = 33
Now, list down the factors of 165
:1,3,5,11,15,33,55,165
Now, list down the factors of 7821
:1,3,9,11,33,79,99,237,711,869,2607,7821
Greatest Common Factor
We found the factors 165,7821 . The biggest common factor number is the GCF number.
So the greatest common factor 165,7821 is 33.
Lets's calculate LCM of 405,8135
5 | 405, 8135 |
81, 1627 |
∴ So the LCM of the given numbers is 5 x 81 x 1627 = 658935
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 33/658935
Therefore, the GCF of Fractions 165/405,7821/8135 is 33/658935
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 405,8135 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(405,8135) = 5
common factors(in case of two or more numbers have common factors) = 1
GCF(405,8135) x common factors =5 x 1 = 5
LCM(405,8135) = ( 405 × 8135 ) / 5
LCM(405,8135) = 3294675 / 5
LCM(405,8135) = 658935
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 165,7821?
The HCF of 165,7821 is 33
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 165/405, 7821/8135?
Answer: GCF of Numerators as per given numbers 165/405, 7821/8135 is
GCF of Numerators i.e. for 165,7821 is 33
LCM of denominators i.e. for 405,8135 is 658935.
Thus, GCF of Fractions is 33/658935.Finally, GCF of Fractions for 165/405, 7821/8135 is 33/658935.