Use our free GCF of Fractions Calculator tool to compute the GCF of 858/414, 406/576 i.e 2/13248 easily. The following is the detailed procedure to determine the greatest common factor of fractions 858/414, 406/576.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 858/414,406/576
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 858/414,406/576, numerators are 858,406
Denominators are 414,576
The GCF of 858,406 is 2 .
LCM of 414,576 is 13248.
The greatest common factor of 858/414,406/576 = [GCF of 858,406]/[LCM of 414,576]= 2/13248
Therefore, the GCF of 858/414,406/576 is 2/13248.
To find the highest common factor of 858,406, we have to find the factors of both numbers and list the highest common factor.
The factors of 858 are 1, 2, 3, 6, 11, 13, 22, 26, 33, 39, 66, 78, 143, 286, 429, 858
The factors of 406 are 1, 2, 7, 14, 29, 58, 203, 406
The HCF of 858,406 is 2.
Lets's calculate GCF of 858,406
2 | 858, 406 |
429, 203 |
∴ So the GCF of the given numbers is 2 = 2
Now, list down the factors of 858
:1,2,3,6,11,13,22,26,33,39,66,78,143,286,429,858
Now, list down the factors of 406
:1,2,7,14,29,58,203,406
Greatest Common Factor
We found the factors 858,406 . The biggest common factor number is the GCF number.
So the greatest common factor 858,406 is 2.
Lets's calculate LCM of 414,576
2 | 414, 576 |
3 | 207, 288 |
3 | 69, 96 |
23, 32 |
∴ So the LCM of the given numbers is 2 x 3 x 3 x 23 x 32 = 13248
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/13248
Therefore, the GCF of Fractions 858/414,406/576 is 2/13248
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 414,576 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(414,576) = 18
common factors(in case of two or more numbers have common factors) = 1
GCF(414,576) x common factors =18 x 1 = 18
LCM(414,576) = ( 414 × 576 ) / 18
LCM(414,576) = 238464 / 18
LCM(414,576) = 13248
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 858,406?
The HCF of 858,406 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 858/414, 406/576?
Answer: GCF of Numerators as per given numbers 858/414, 406/576 is
GCF of Numerators i.e. for 858,406 is 2
LCM of denominators i.e. for 414,576 is 13248.
Thus, GCF of Fractions is 2/13248.Finally, GCF of Fractions for 858/414, 406/576 is 2/13248.