Use our free GCF of Fractions Calculator tool to compute the GCF of 14/366, 82/105, 822/135 i.e 2/115290 easily. The following is the detailed procedure to determine the greatest common factor of fractions 14/366, 82/105, 822/135.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 14/366,82/105,822/135
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 14/366,82/105,822/135, numerators are 14,82,822
Denominators are 366,105,135
The GCF of 14,82,822 is 2 .
LCM of 366,105,135 is 115290.
The greatest common factor of 14/366,82/105,822/135 = [GCF of 14,82,822]/[LCM of 366,105,135]= 2/115290
Therefore, the GCF of 14/366,82/105,822/135 is 2/115290.
To find the highest common factor of 14,82,822, we have to find the factors of both numbers and list the highest common factor.
The factors of 14 are 1, 2, 7, 14
The factors of 82 are 1, 2, 41, 82
The factors of 822 are 1, 2, 3, 6, 137, 274, 411, 822
The HCF of 14,82,822 is 2.
Lets's calculate GCF of 14,82,822
2 | 14, 82, 822 |
7, 41, 411 |
∴ So the GCF of the given numbers is 2 = 2
Now, list down the factors of 14
:1,2,7,14
Now, list down the factors of 82
:1,2,41,82
Now, list down the factors of 822
:1,2,3,6,137,274,411,822
Greatest Common Factor
We found the factors 14,82,822 . The biggest common factor number is the GCF number.
So the greatest common factor 14,82,822 is 2.
Lets's calculate LCM of 366,105,135
3 | 366, 105, 135 |
5 | 122, 35, 45 |
122, 7, 9 |
∴ So the LCM of the given numbers is 3 x 5 x 122 x 7 x 9 = 115290
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/115290
Therefore, the GCF of Fractions 14/366,82/105,822/135 is 2/115290
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 366,105,135 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(366,105,135) = 3
common factors(in case of two or more numbers have common factors) = 15
GCF(366,105,135) x common factors =3 x 15 = 45
LCM(366,105,135) = ( 366 × 105 × 135 ) / 45
LCM(366,105,135) = 5188050 / 45
LCM(366,105,135) = 115290
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 14,82,822?
The HCF of 14,82,822 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 14/366, 82/105, 822/135?
Answer: GCF of Numerators as per given numbers 14/366, 82/105, 822/135 is
GCF of Numerators i.e. for 14,82,822 is 2
LCM of denominators i.e. for 366,105,135 is 115290.
Thus, GCF of Fractions is 2/115290.Finally, GCF of Fractions for 14/366, 82/105, 822/135 is 2/115290.