Use our free GCF of Fractions Calculator tool to compute the GCF of 544/414, 298/997 i.e 2/412758 easily. The following is the detailed procedure to determine the greatest common factor of fractions 544/414, 298/997.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 544/414,298/997
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 544/414,298/997, numerators are 544,298
Denominators are 414,997
The GCF of 544,298 is 2 .
LCM of 414,997 is 412758.
The greatest common factor of 544/414,298/997 = [GCF of 544,298]/[LCM of 414,997]= 2/412758
Therefore, the GCF of 544/414,298/997 is 2/412758.
To find the highest common factor of 544,298, we have to find the factors of both numbers and list the highest common factor.
The factors of 544 are 1, 2, 4, 8, 16, 17, 32, 34, 68, 136, 272, 544
The factors of 298 are 1, 2, 149, 298
The HCF of 544,298 is 2.
Lets's calculate GCF of 544,298
2 | 544, 298 |
272, 149 |
∴ So the GCF of the given numbers is 2 = 2
Now, list down the factors of 544
:1,2,4,8,16,17,32,34,68,136,272,544
Now, list down the factors of 298
:1,2,149,298
Greatest Common Factor
We found the factors 544,298 . The biggest common factor number is the GCF number.
So the greatest common factor 544,298 is 2.
Lets's calculate LCM of 414,997
Given numbers has no common factors except 1. So, there LCM is their product i.e 412758
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/412758
Therefore, the GCF of Fractions 544/414,298/997 is 2/412758
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 414,997 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(414,997) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(414,997) x common factors =1 x 1 = 1
LCM(414,997) = ( 414 × 997 ) / 1
LCM(414,997) = 412758 / 1
LCM(414,997) = 412758
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 544,298?
The HCF of 544,298 is 2
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 544/414, 298/997?
Answer: GCF of Numerators as per given numbers 544/414, 298/997 is
GCF of Numerators i.e. for 544,298 is 2
LCM of denominators i.e. for 414,997 is 412758.
Thus, GCF of Fractions is 2/412758.Finally, GCF of Fractions for 544/414, 298/997 is 2/412758.