Use our free GCF of Fractions Calculator tool to compute the GCF of 412/260, 658/839 i.e 2/218140 easily. The following is the detailed procedure to determine the greatest common factor of fractions 412/260, 658/839.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 412/260,658/839
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 412/260,658/839, numerators are 412,658
Denominators are 260,839
The GCF of 412,658 is 2 .
LCM of 260,839 is 218140.
The greatest common factor of 412/260,658/839 = [GCF of 412,658]/[LCM of 260,839]= 2/218140
Therefore, the GCF of 412/260,658/839 is 2/218140.
To find the highest common factor of 412,658, we have to find the factors of both numbers and list the highest common factor.
The factors of 412 are 1, 2, 4, 103, 206, 412
The factors of 658 are 1, 2, 7, 14, 47, 94, 329, 658
The HCF of 412,658 is 2.
Lets's calculate GCF of 412,658
2 | 412, 658 |
206, 329 |
∴ So the GCF of the given numbers is 2 = 2
Now, list down the factors of 412
:1,2,4,103,206,412
Now, list down the factors of 658
:1,2,7,14,47,94,329,658
Greatest Common Factor
We found the factors 412,658 . The biggest common factor number is the GCF number.
So the greatest common factor 412,658 is 2.
Lets's calculate LCM of 260,839
Given numbers has no common factors except 1. So, there LCM is their product i.e 218140
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/218140
Therefore, the GCF of Fractions 412/260,658/839 is 2/218140
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 260,839 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(260,839) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(260,839) x common factors =1 x 1 = 1
LCM(260,839) = ( 260 × 839 ) / 1
LCM(260,839) = 218140 / 1
LCM(260,839) = 218140
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 412,658?
The HCF of 412,658 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 412/260, 658/839?
Answer: GCF of Numerators as per given numbers 412/260, 658/839 is
GCF of Numerators i.e. for 412,658 is 2
LCM of denominators i.e. for 260,839 is 218140.
Thus, GCF of Fractions is 2/218140.Finally, GCF of Fractions for 412/260, 658/839 is 2/218140.