Use our free GCF of Fractions Calculator tool to compute the GCF of 412/986, 609/208 i.e 1/102544 easily. The following is the detailed procedure to determine the greatest common factor of fractions 412/986, 609/208.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 412/986,609/208
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 412/986,609/208, numerators are 412,609
Denominators are 986,208
The GCF of 412,609 is 1 .
LCM of 986,208 is 102544.
The greatest common factor of 412/986,609/208 = [GCF of 412,609]/[LCM of 986,208]= 1/102544
Therefore, the GCF of 412/986,609/208 is 1/102544.
To find the highest common factor of 412,609, 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 609 are 1, 3, 7, 21, 29, 87, 203, 609
The HCF of 412,609 is 1.
Lets's calculate GCF of 412,609
∴ So GCF of numbers is 1 because of no common factors present between them.
Now, list down the factors of 412
:1,2,4,103,206,412
Now, list down the factors of 609
:1,3,7,21,29,87,203,609
Greatest Common Factor
We found the factors 412,609 . The biggest common factor number is the GCF number.
So the greatest common factor 412,609 is 1.
Lets's calculate LCM of 986,208
2 | 986, 208 |
493, 104 |
∴ So the LCM of the given numbers is 2 x 493 x 104 = 102544
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/102544
Therefore, the GCF of Fractions 412/986,609/208 is 1/102544
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 986,208 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(986,208) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(986,208) x common factors =2 x 1 = 2
LCM(986,208) = ( 986 × 208 ) / 2
LCM(986,208) = 205088 / 2
LCM(986,208) = 102544
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 412,609?
The HCF of 412,609 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 412/986, 609/208?
Answer: GCF of Numerators as per given numbers 412/986, 609/208 is
GCF of Numerators i.e. for 412,609 is 1
LCM of denominators i.e. for 986,208 is 102544.
Thus, GCF of Fractions is 1/102544.Finally, GCF of Fractions for 412/986, 609/208 is 1/102544.