Use our free GCF of Fractions Calculator tool to compute the GCF of 474/372, 405/311 i.e 3/115692 easily. The following is the detailed procedure to determine the greatest common factor of fractions 474/372, 405/311.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 474/372,405/311
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 474/372,405/311, numerators are 474,405
Denominators are 372,311
The GCF of 474,405 is 3 .
LCM of 372,311 is 115692.
The greatest common factor of 474/372,405/311 = [GCF of 474,405]/[LCM of 372,311]= 3/115692
Therefore, the GCF of 474/372,405/311 is 3/115692.
To find the highest common factor of 474,405, we have to find the factors of both numbers and list the highest common factor.
The factors of 474 are 1, 2, 3, 6, 79, 158, 237, 474
The factors of 405 are 1, 3, 5, 9, 15, 27, 45, 81, 135, 405
The HCF of 474,405 is 3.
Lets's calculate GCF of 474,405
3 | 474, 405 |
158, 135 |
∴ So the GCF of the given numbers is 3 = 3
Now, list down the factors of 474
:1,2,3,6,79,158,237,474
Now, list down the factors of 405
:1,3,5,9,15,27,45,81,135,405
Greatest Common Factor
We found the factors 474,405 . The biggest common factor number is the GCF number.
So the greatest common factor 474,405 is 3.
Lets's calculate LCM of 372,311
Given numbers has no common factors except 1. So, there LCM is their product i.e 115692
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 3/115692
Therefore, the GCF of Fractions 474/372,405/311 is 3/115692
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 372,311 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(372,311) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(372,311) x common factors =1 x 1 = 1
LCM(372,311) = ( 372 × 311 ) / 1
LCM(372,311) = 115692 / 1
LCM(372,311) = 115692
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 474,405?
The HCF of 474,405 is 3
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 474/372, 405/311?
Answer: GCF of Numerators as per given numbers 474/372, 405/311 is
GCF of Numerators i.e. for 474,405 is 3
LCM of denominators i.e. for 372,311 is 115692.
Thus, GCF of Fractions is 3/115692.Finally, GCF of Fractions for 474/372, 405/311 is 3/115692.