Use our free GCF of Fractions Calculator tool to compute the GCF of 221/553, 309/289 i.e 1/159817 easily. The following is the detailed procedure to determine the greatest common factor of fractions 221/553, 309/289.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 221/553,309/289
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 221/553,309/289, numerators are 221,309
Denominators are 553,289
The GCF of 221,309 is 1 .
LCM of 553,289 is 159817.
The greatest common factor of 221/553,309/289 = [GCF of 221,309]/[LCM of 553,289]= 1/159817
Therefore, the GCF of 221/553,309/289 is 1/159817.
To find the highest common factor of 221,309, we have to find the factors of both numbers and list the highest common factor.
The factors of 221 are 1, 13, 17, 221
The factors of 309 are 1, 3, 103, 309
The HCF of 221,309 is 1.
Lets's calculate GCF of 221,309
∴ So GCF of numbers is 1 because of no common factors present between them.
Now, list down the factors of 221
:1,13,17,221
Now, list down the factors of 309
:1,3,103,309
Greatest Common Factor
We found the factors 221,309 . The biggest common factor number is the GCF number.
So the greatest common factor 221,309 is 1.
Lets's calculate LCM of 553,289
Given numbers has no common factors except 1. So, there LCM is their product i.e 159817
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/159817
Therefore, the GCF of Fractions 221/553,309/289 is 1/159817
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 553,289 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(553,289) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(553,289) x common factors =1 x 1 = 1
LCM(553,289) = ( 553 × 289 ) / 1
LCM(553,289) = 159817 / 1
LCM(553,289) = 159817
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 221,309?
The HCF of 221,309 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 221/553, 309/289?
Answer: GCF of Numerators as per given numbers 221/553, 309/289 is
GCF of Numerators i.e. for 221,309 is 1
LCM of denominators i.e. for 553,289 is 159817.
Thus, GCF of Fractions is 1/159817.Finally, GCF of Fractions for 221/553, 309/289 is 1/159817.