Use our free GCF of Fractions Calculator tool to compute the GCF of 309/758, 221/584 i.e 1/221336 easily. The following is the detailed procedure to determine the greatest common factor of fractions 309/758, 221/584.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 309/758,221/584
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 309/758,221/584, numerators are 309,221
Denominators are 758,584
The GCF of 309,221 is 1 .
LCM of 758,584 is 221336.
The greatest common factor of 309/758,221/584 = [GCF of 309,221]/[LCM of 758,584]= 1/221336
Therefore, the GCF of 309/758,221/584 is 1/221336.
To find the highest common factor of 309,221, we have to find the factors of both numbers and list the highest common factor.
The factors of 309 are 1, 3, 103, 309
The factors of 221 are 1, 13, 17, 221
The HCF of 309,221 is 1.
Lets's calculate GCF of 309,221
∴ So GCF of numbers is 1 because of no common factors present between them.
Now, list down the factors of 309
:1,3,103,309
Now, list down the factors of 221
:1,13,17,221
Greatest Common Factor
We found the factors 309,221 . The biggest common factor number is the GCF number.
So the greatest common factor 309,221 is 1.
Lets's calculate LCM of 758,584
2 | 758, 584 |
379, 292 |
∴ So the LCM of the given numbers is 2 x 379 x 292 = 221336
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/221336
Therefore, the GCF of Fractions 309/758,221/584 is 1/221336
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 758,584 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(758,584) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(758,584) x common factors =2 x 1 = 2
LCM(758,584) = ( 758 × 584 ) / 2
LCM(758,584) = 442672 / 2
LCM(758,584) = 221336
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 309,221?
The HCF of 309,221 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 309/758, 221/584?
Answer: GCF of Numerators as per given numbers 309/758, 221/584 is
GCF of Numerators i.e. for 309,221 is 1
LCM of denominators i.e. for 758,584 is 221336.
Thus, GCF of Fractions is 1/221336.Finally, GCF of Fractions for 309/758, 221/584 is 1/221336.