Use our free GCF of Fractions Calculator tool to compute the GCF of 22/17, 204/31, 297/205 i.e 1/108035 easily. The following is the detailed procedure to determine the greatest common factor of fractions 22/17, 204/31, 297/205.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 22/17,204/31,297/205
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 22/17,204/31,297/205, numerators are 22,204,297
Denominators are 17,31,205
The GCF of 22,204,297 is 1 .
LCM of 17,31,205 is 108035.
The greatest common factor of 22/17,204/31,297/205 = [GCF of 22,204,297]/[LCM of 17,31,205]= 1/108035
Therefore, the GCF of 22/17,204/31,297/205 is 1/108035.
To find the highest common factor of 22,204,297, we have to find the factors of both numbers and list the highest common factor.
The factors of 22 are 1, 2, 11, 22
The factors of 204 are 1, 2, 3, 4, 6, 12, 17, 34, 51, 68, 102, 204
The factors of 297 are 1, 3, 9, 11, 27, 33, 99, 297
The HCF of 22,204,297 is 1.
Lets's calculate GCF of 22,204,297
∴ So GCF of numbers is 1 because of no common factors present between them.
Now, list down the factors of 22
:1,2,11,22
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 297
:1,3,9,11,27,33,99,297
Greatest Common Factor
We found the factors 22,204,297 . The biggest common factor number is the GCF number.
So the greatest common factor 22,204,297 is 1.
Lets's calculate LCM of 17,31,205
Given numbers has no common factors except 1. So, there LCM is their product i.e 108035
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/108035
Therefore, the GCF of Fractions 22/17,204/31,297/205 is 1/108035
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 17,31,205 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(17,31,205) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(17,31,205) x common factors =1 x 1 = 1
LCM(17,31,205) = ( 17 × 31 × 205 ) / 1
LCM(17,31,205) = 108035 / 1
LCM(17,31,205) = 108035
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 22,204,297?
The HCF of 22,204,297 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 22/17, 204/31, 297/205?
Answer: GCF of Numerators as per given numbers 22/17, 204/31, 297/205 is
GCF of Numerators i.e. for 22,204,297 is 1
LCM of denominators i.e. for 17,31,205 is 108035.
Thus, GCF of Fractions is 1/108035.Finally, GCF of Fractions for 22/17, 204/31, 297/205 is 1/108035.