Use our free GCF of Fractions Calculator tool to compute the GCF of 204/32, 659/810 i.e 1/12960 easily. The following is the detailed procedure to determine the greatest common factor of fractions 204/32, 659/810.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 204/32,659/810
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 204/32,659/810, numerators are 204,659
Denominators are 32,810
The GCF of 204,659 is 1 .
LCM of 32,810 is 12960.
The greatest common factor of 204/32,659/810 = [GCF of 204,659]/[LCM of 32,810]= 1/12960
Therefore, the GCF of 204/32,659/810 is 1/12960.
To find the highest common factor of 204,659, 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 659 are 1, 659
The HCF of 204,659 is 1.
Lets's calculate GCF of 204,659
∴ So GCF of numbers is 1 because of no common factors present between them.
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 659
:1,659
Greatest Common Factor
We found the factors 204,659 . The biggest common factor number is the GCF number.
So the greatest common factor 204,659 is 1.
Lets's calculate LCM of 32,810
2 | 32, 810 |
16, 405 |
∴ So the LCM of the given numbers is 2 x 16 x 405 = 12960
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/12960
Therefore, the GCF of Fractions 204/32,659/810 is 1/12960
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 32,810 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(32,810) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(32,810) x common factors =2 x 1 = 2
LCM(32,810) = ( 32 × 810 ) / 2
LCM(32,810) = 25920 / 2
LCM(32,810) = 12960
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 204,659?
The HCF of 204,659 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 204/32, 659/810?
Answer: GCF of Numerators as per given numbers 204/32, 659/810 is
GCF of Numerators i.e. for 204,659 is 1
LCM of denominators i.e. for 32,810 is 12960.
Thus, GCF of Fractions is 1/12960.Finally, GCF of Fractions for 204/32, 659/810 is 1/12960.