Use our free GCF of Fractions Calculator tool to compute the GCF of 205/309, 204/964 i.e 1/297876 easily. The following is the detailed procedure to determine the greatest common factor of fractions 205/309, 204/964.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 205/309,204/964
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 205/309,204/964, numerators are 205,204
Denominators are 309,964
The GCF of 205,204 is 1 .
LCM of 309,964 is 297876.
The greatest common factor of 205/309,204/964 = [GCF of 205,204]/[LCM of 309,964]= 1/297876
Therefore, the GCF of 205/309,204/964 is 1/297876.
To find the highest common factor of 205,204, we have to find the factors of both numbers and list the highest common factor.
The factors of 205 are 1, 5, 41, 205
The factors of 204 are 1, 2, 3, 4, 6, 12, 17, 34, 51, 68, 102, 204
The HCF of 205,204 is 1.
Lets's calculate GCF of 205,204
∴ So GCF of numbers is 1 because of no common factors present between them.
Now, list down the factors of 205
:1,5,41,205
Now, list down the factors of 204
:1,2,3,4,6,12,17,34,51,68,102,204
Greatest Common Factor
We found the factors 205,204 . The biggest common factor number is the GCF number.
So the greatest common factor 205,204 is 1.
Lets's calculate LCM of 309,964
Given numbers has no common factors except 1. So, there LCM is their product i.e 297876
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/297876
Therefore, the GCF of Fractions 205/309,204/964 is 1/297876
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 309,964 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(309,964) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(309,964) x common factors =1 x 1 = 1
LCM(309,964) = ( 309 × 964 ) / 1
LCM(309,964) = 297876 / 1
LCM(309,964) = 297876
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 205,204?
The HCF of 205,204 is 1
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 205/309, 204/964?
Answer: GCF of Numerators as per given numbers 205/309, 204/964 is
GCF of Numerators i.e. for 205,204 is 1
LCM of denominators i.e. for 309,964 is 297876.
Thus, GCF of Fractions is 1/297876.Finally, GCF of Fractions for 205/309, 204/964 is 1/297876.