Use our free GCF of Fractions Calculator tool to compute the GCF of 212/469, 198/576 i.e 2/270144 easily. The following is the detailed procedure to determine the greatest common factor of fractions 212/469, 198/576.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 212/469,198/576
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 212/469,198/576, numerators are 212,198
Denominators are 469,576
The GCF of 212,198 is 2 .
LCM of 469,576 is 270144.
The greatest common factor of 212/469,198/576 = [GCF of 212,198]/[LCM of 469,576]= 2/270144
Therefore, the GCF of 212/469,198/576 is 2/270144.
To find the highest common factor of 212,198, we have to find the factors of both numbers and list the highest common factor.
The factors of 212 are 1, 2, 4, 53, 106, 212
The factors of 198 are 1, 2, 3, 6, 9, 11, 18, 22, 33, 66, 99, 198
The HCF of 212,198 is 2.
Lets's calculate GCF of 212,198
2 | 212, 198 |
106, 99 |
∴ So the GCF of the given numbers is 2 = 2
Now, list down the factors of 212
:1,2,4,53,106,212
Now, list down the factors of 198
:1,2,3,6,9,11,18,22,33,66,99,198
Greatest Common Factor
We found the factors 212,198 . The biggest common factor number is the GCF number.
So the greatest common factor 212,198 is 2.
Lets's calculate LCM of 469,576
Given numbers has no common factors except 1. So, there LCM is their product i.e 270144
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/270144
Therefore, the GCF of Fractions 212/469,198/576 is 2/270144
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 469,576 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(469,576) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(469,576) x common factors =1 x 1 = 1
LCM(469,576) = ( 469 × 576 ) / 1
LCM(469,576) = 270144 / 1
LCM(469,576) = 270144
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 212,198?
The HCF of 212,198 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 212/469, 198/576?
Answer: GCF of Numerators as per given numbers 212/469, 198/576 is
GCF of Numerators i.e. for 212,198 is 2
LCM of denominators i.e. for 469,576 is 270144.
Thus, GCF of Fractions is 2/270144.Finally, GCF of Fractions for 212/469, 198/576 is 2/270144.