Use our free GCF of Fractions Calculator tool to compute the GCF of 409/378, 298/802 i.e 1/151578 easily. The following is the detailed procedure to determine the greatest common factor of fractions 409/378, 298/802.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 409/378,298/802
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 409/378,298/802, numerators are 409,298
Denominators are 378,802
The GCF of 409,298 is 1 .
LCM of 378,802 is 151578.
The greatest common factor of 409/378,298/802 = [GCF of 409,298]/[LCM of 378,802]= 1/151578
Therefore, the GCF of 409/378,298/802 is 1/151578.
To find the highest common factor of 409,298, we have to find the factors of both numbers and list the highest common factor.
The factors of 409 are 1, 409
The factors of 298 are 1, 2, 149, 298
The HCF of 409,298 is 1.
Lets's calculate GCF of 409,298
∴ So GCF of numbers is 1 because of no common factors present between them.
Now, list down the factors of 409
:1,409
Now, list down the factors of 298
:1,2,149,298
Greatest Common Factor
We found the factors 409,298 . The biggest common factor number is the GCF number.
So the greatest common factor 409,298 is 1.
Lets's calculate LCM of 378,802
2 | 378, 802 |
189, 401 |
∴ So the LCM of the given numbers is 2 x 189 x 401 = 151578
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/151578
Therefore, the GCF of Fractions 409/378,298/802 is 1/151578
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 378,802 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(378,802) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(378,802) x common factors =2 x 1 = 2
LCM(378,802) = ( 378 × 802 ) / 2
LCM(378,802) = 303156 / 2
LCM(378,802) = 151578
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 409,298?
The HCF of 409,298 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 409/378, 298/802?
Answer: GCF of Numerators as per given numbers 409/378, 298/802 is
GCF of Numerators i.e. for 409,298 is 1
LCM of denominators i.e. for 378,802 is 151578.
Thus, GCF of Fractions is 1/151578.Finally, GCF of Fractions for 409/378, 298/802 is 1/151578.