Use our free GCF of Fractions Calculator tool to compute the GCF of 498/575, 415/261 i.e 83/150075 easily. The following is the detailed procedure to determine the greatest common factor of fractions 498/575, 415/261.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 498/575,415/261
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 498/575,415/261, numerators are 498,415
Denominators are 575,261
The GCF of 498,415 is 83 .
LCM of 575,261 is 150075.
The greatest common factor of 498/575,415/261 = [GCF of 498,415]/[LCM of 575,261]= 83/150075
Therefore, the GCF of 498/575,415/261 is 83/150075.
To find the highest common factor of 498,415, we have to find the factors of both numbers and list the highest common factor.
The factors of 498 are 1, 2, 3, 6, 83, 166, 249, 498
The factors of 415 are 1, 5, 83, 415
The HCF of 498,415 is 83.
Lets's calculate GCF of 498,415
83 | 498, 415 |
6, 5 |
∴ So the GCF of the given numbers is 83 = 83
Now, list down the factors of 498
:1,2,3,6,83,166,249,498
Now, list down the factors of 415
:1,5,83,415
Greatest Common Factor
We found the factors 498,415 . The biggest common factor number is the GCF number.
So the greatest common factor 498,415 is 83.
Lets's calculate LCM of 575,261
Given numbers has no common factors except 1. So, there LCM is their product i.e 150075
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 83/150075
Therefore, the GCF of Fractions 498/575,415/261 is 83/150075
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 575,261 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(575,261) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(575,261) x common factors =1 x 1 = 1
LCM(575,261) = ( 575 × 261 ) / 1
LCM(575,261) = 150075 / 1
LCM(575,261) = 150075
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 498,415?
The HCF of 498,415 is 83
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 498/575, 415/261?
Answer: GCF of Numerators as per given numbers 498/575, 415/261 is
GCF of Numerators i.e. for 498,415 is 83
LCM of denominators i.e. for 575,261 is 150075.
Thus, GCF of Fractions is 83/150075.Finally, GCF of Fractions for 498/575, 415/261 is 83/150075.