Use our free GCF of Fractions Calculator tool to compute the GCF of 410/133, 421/285 i.e 1/1995 easily. The following is the detailed procedure to determine the greatest common factor of fractions 410/133, 421/285.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 410/133,421/285
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 410/133,421/285, numerators are 410,421
Denominators are 133,285
The GCF of 410,421 is 1 .
LCM of 133,285 is 1995.
The greatest common factor of 410/133,421/285 = [GCF of 410,421]/[LCM of 133,285]= 1/1995
Therefore, the GCF of 410/133,421/285 is 1/1995.
To find the highest common factor of 410,421, we have to find the factors of both numbers and list the highest common factor.
The factors of 410 are 1, 2, 5, 10, 41, 82, 205, 410
The factors of 421 are 1, 421
The HCF of 410,421 is 1.
Lets's calculate GCF of 410,421
∴ So GCF of numbers is 1 because of no common factors present between them.
Now, list down the factors of 410
:1,2,5,10,41,82,205,410
Now, list down the factors of 421
:1,421
Greatest Common Factor
We found the factors 410,421 . The biggest common factor number is the GCF number.
So the greatest common factor 410,421 is 1.
Lets's calculate LCM of 133,285
19 | 133, 285 |
7, 15 |
∴ So the LCM of the given numbers is 19 x 7 x 15 = 1995
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/1995
Therefore, the GCF of Fractions 410/133,421/285 is 1/1995
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 133,285 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(133,285) = 19
common factors(in case of two or more numbers have common factors) = 1
GCF(133,285) x common factors =19 x 1 = 19
LCM(133,285) = ( 133 × 285 ) / 19
LCM(133,285) = 37905 / 19
LCM(133,285) = 1995
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 410,421?
The HCF of 410,421 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 410/133, 421/285?
Answer: GCF of Numerators as per given numbers 410/133, 421/285 is
GCF of Numerators i.e. for 410,421 is 1
LCM of denominators i.e. for 133,285 is 1995.
Thus, GCF of Fractions is 1/1995.Finally, GCF of Fractions for 410/133, 421/285 is 1/1995.