Use our free GCF of Fractions Calculator tool to compute the GCF of 215/782, 410/631 i.e 5/493442 easily. The following is the detailed procedure to determine the greatest common factor of fractions 215/782, 410/631.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 215/782,410/631
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 215/782,410/631, numerators are 215,410
Denominators are 782,631
The GCF of 215,410 is 5 .
LCM of 782,631 is 493442.
The greatest common factor of 215/782,410/631 = [GCF of 215,410]/[LCM of 782,631]= 5/493442
Therefore, the GCF of 215/782,410/631 is 5/493442.
To find the highest common factor of 215,410, we have to find the factors of both numbers and list the highest common factor.
The factors of 215 are 1, 5, 43, 215
The factors of 410 are 1, 2, 5, 10, 41, 82, 205, 410
The HCF of 215,410 is 5.
Lets's calculate GCF of 215,410
5 | 215, 410 |
43, 82 |
∴ So the GCF of the given numbers is 5 = 5
Now, list down the factors of 215
:1,5,43,215
Now, list down the factors of 410
:1,2,5,10,41,82,205,410
Greatest Common Factor
We found the factors 215,410 . The biggest common factor number is the GCF number.
So the greatest common factor 215,410 is 5.
Lets's calculate LCM of 782,631
Given numbers has no common factors except 1. So, there LCM is their product i.e 493442
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 5/493442
Therefore, the GCF of Fractions 215/782,410/631 is 5/493442
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 782,631 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(782,631) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(782,631) x common factors =1 x 1 = 1
LCM(782,631) = ( 782 × 631 ) / 1
LCM(782,631) = 493442 / 1
LCM(782,631) = 493442
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 215,410?
The HCF of 215,410 is 5
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 215/782, 410/631?
Answer: GCF of Numerators as per given numbers 215/782, 410/631 is
GCF of Numerators i.e. for 215,410 is 5
LCM of denominators i.e. for 782,631 is 493442.
Thus, GCF of Fractions is 5/493442.Finally, GCF of Fractions for 215/782, 410/631 is 5/493442.