Use our free GCF of Fractions Calculator tool to compute the GCF of 204/166, 636/116 i.e 12/9628 easily. The following is the detailed procedure to determine the greatest common factor of fractions 204/166, 636/116.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 204/166,636/116
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 204/166,636/116, numerators are 204,636
Denominators are 166,116
The GCF of 204,636 is 12 .
LCM of 166,116 is 9628.
The greatest common factor of 204/166,636/116 = [GCF of 204,636]/[LCM of 166,116]= 12/9628
Therefore, the GCF of 204/166,636/116 is 12/9628.
To find the highest common factor of 204,636, we have to find the factors of both numbers and list the highest common factor.
The factors of 204 are 1, 2, 3, 4, 6, 12, 17, 34, 51, 68, 102, 204
The factors of 636 are 1, 2, 3, 4, 6, 12, 53, 106, 159, 212, 318, 636
The HCF of 204,636 is 12.
Lets's calculate GCF of 204,636
2 | 204, 636 |
2 | 102, 318 |
3 | 51, 159 |
17, 53 |
∴ So the GCF of the given numbers is 2 x 2 x 3 = 12
Now, list down the factors of 204
:1,2,3,4,6,12,17,34,51,68,102,204
Now, list down the factors of 636
:1,2,3,4,6,12,53,106,159,212,318,636
Greatest Common Factor
We found the factors 204,636 . The biggest common factor number is the GCF number.
So the greatest common factor 204,636 is 12.
Lets's calculate LCM of 166,116
2 | 166, 116 |
83, 58 |
∴ So the LCM of the given numbers is 2 x 83 x 58 = 9628
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 12/9628
Therefore, the GCF of Fractions 204/166,636/116 is 12/9628
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 166,116 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(166,116) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(166,116) x common factors =2 x 1 = 2
LCM(166,116) = ( 166 × 116 ) / 2
LCM(166,116) = 19256 / 2
LCM(166,116) = 9628
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 204,636?
The HCF of 204,636 is 12
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 204/166, 636/116?
Answer: GCF of Numerators as per given numbers 204/166, 636/116 is
GCF of Numerators i.e. for 204,636 is 12
LCM of denominators i.e. for 166,116 is 9628.
Thus, GCF of Fractions is 12/9628.Finally, GCF of Fractions for 204/166, 636/116 is 12/9628.