Use our free GCF of Fractions Calculator tool to compute the GCF of 436/586, 109/344 i.e 109/100792 easily. The following is the detailed procedure to determine the greatest common factor of fractions 436/586, 109/344.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 436/586,109/344
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 436/586,109/344, numerators are 436,109
Denominators are 586,344
The GCF of 436,109 is 109 .
LCM of 586,344 is 100792.
The greatest common factor of 436/586,109/344 = [GCF of 436,109]/[LCM of 586,344]= 109/100792
Therefore, the GCF of 436/586,109/344 is 109/100792.
To find the highest common factor of 436,109, we have to find the factors of both numbers and list the highest common factor.
The factors of 436 are 1, 2, 4, 109, 218, 436
The factors of 109 are 1, 109
The HCF of 436,109 is 109.
Lets's calculate GCF of 436,109
109 | 436, 109 |
4, 1 |
∴ So the GCF of the given numbers is 109 = 109
Now, list down the factors of 436
:1,2,4,109,218,436
Now, list down the factors of 109
:1,109
Greatest Common Factor
We found the factors 436,109 . The biggest common factor number is the GCF number.
So the greatest common factor 436,109 is 109.
Lets's calculate LCM of 586,344
2 | 586, 344 |
293, 172 |
∴ So the LCM of the given numbers is 2 x 293 x 172 = 100792
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 109/100792
Therefore, the GCF of Fractions 436/586,109/344 is 109/100792
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 586,344 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(586,344) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(586,344) x common factors =2 x 1 = 2
LCM(586,344) = ( 586 × 344 ) / 2
LCM(586,344) = 201584 / 2
LCM(586,344) = 100792
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 436,109?
The HCF of 436,109 is 109
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 436/586, 109/344?
Answer: GCF of Numerators as per given numbers 436/586, 109/344 is
GCF of Numerators i.e. for 436,109 is 109
LCM of denominators i.e. for 586,344 is 100792.
Thus, GCF of Fractions is 109/100792.Finally, GCF of Fractions for 436/586, 109/344 is 109/100792.