Use our free GCF of Fractions Calculator tool to compute the GCF of 405/580, 989/410 i.e 1/23780 easily. The following is the detailed procedure to determine the greatest common factor of fractions 405/580, 989/410.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 405/580,989/410
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 405/580,989/410, numerators are 405,989
Denominators are 580,410
The GCF of 405,989 is 1 .
LCM of 580,410 is 23780.
The greatest common factor of 405/580,989/410 = [GCF of 405,989]/[LCM of 580,410]= 1/23780
Therefore, the GCF of 405/580,989/410 is 1/23780.
To find the highest common factor of 405,989, we have to find the factors of both numbers and list the highest common factor.
The factors of 405 are 1, 3, 5, 9, 15, 27, 45, 81, 135, 405
The factors of 989 are 1, 23, 43, 989
The HCF of 405,989 is 1.
Lets's calculate GCF of 405,989
∴ So GCF of numbers is 1 because of no common factors present between them.
Now, list down the factors of 405
:1,3,5,9,15,27,45,81,135,405
Now, list down the factors of 989
:1,23,43,989
Greatest Common Factor
We found the factors 405,989 . The biggest common factor number is the GCF number.
So the greatest common factor 405,989 is 1.
Lets's calculate LCM of 580,410
2 | 580, 410 |
5 | 290, 205 |
58, 41 |
∴ So the LCM of the given numbers is 2 x 5 x 58 x 41 = 23780
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/23780
Therefore, the GCF of Fractions 405/580,989/410 is 1/23780
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 580,410 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(580,410) = 10
common factors(in case of two or more numbers have common factors) = 1
GCF(580,410) x common factors =10 x 1 = 10
LCM(580,410) = ( 580 × 410 ) / 10
LCM(580,410) = 237800 / 10
LCM(580,410) = 23780
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 405,989?
The HCF of 405,989 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 405/580, 989/410?
Answer: GCF of Numerators as per given numbers 405/580, 989/410 is
GCF of Numerators i.e. for 405,989 is 1
LCM of denominators i.e. for 580,410 is 23780.
Thus, GCF of Fractions is 1/23780.Finally, GCF of Fractions for 405/580, 989/410 is 1/23780.