Use our free GCF of Fractions Calculator tool to compute the GCF of 109/407, 598/315 i.e 1/128205 easily. The following is the detailed procedure to determine the greatest common factor of fractions 109/407, 598/315.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 109/407,598/315
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 109/407,598/315, numerators are 109,598
Denominators are 407,315
The GCF of 109,598 is 1 .
LCM of 407,315 is 128205.
The greatest common factor of 109/407,598/315 = [GCF of 109,598]/[LCM of 407,315]= 1/128205
Therefore, the GCF of 109/407,598/315 is 1/128205.
To find the highest common factor of 109,598, we have to find the factors of both numbers and list the highest common factor.
The factors of 109 are 1, 109
The factors of 598 are 1, 2, 13, 23, 26, 46, 299, 598
The HCF of 109,598 is 1.
Lets's calculate GCF of 109,598
∴ So GCF of numbers is 1 because of no common factors present between them.
Now, list down the factors of 109
:1,109
Now, list down the factors of 598
:1,2,13,23,26,46,299,598
Greatest Common Factor
We found the factors 109,598 . The biggest common factor number is the GCF number.
So the greatest common factor 109,598 is 1.
Lets's calculate LCM of 407,315
Given numbers has no common factors except 1. So, there LCM is their product i.e 128205
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/128205
Therefore, the GCF of Fractions 109/407,598/315 is 1/128205
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 407,315 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(407,315) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(407,315) x common factors =1 x 1 = 1
LCM(407,315) = ( 407 × 315 ) / 1
LCM(407,315) = 128205 / 1
LCM(407,315) = 128205
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 109,598?
The HCF of 109,598 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 109/407, 598/315?
Answer: GCF of Numerators as per given numbers 109/407, 598/315 is
GCF of Numerators i.e. for 109,598 is 1
LCM of denominators i.e. for 407,315 is 128205.
Thus, GCF of Fractions is 1/128205.Finally, GCF of Fractions for 109/407, 598/315 is 1/128205.