Use our free GCF of Fractions Calculator tool to compute the GCF of 410/798, 686/400 i.e 2/159600 easily. The following is the detailed procedure to determine the greatest common factor of fractions 410/798, 686/400.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 410/798,686/400
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 410/798,686/400, numerators are 410,686
Denominators are 798,400
The GCF of 410,686 is 2 .
LCM of 798,400 is 159600.
The greatest common factor of 410/798,686/400 = [GCF of 410,686]/[LCM of 798,400]= 2/159600
Therefore, the GCF of 410/798,686/400 is 2/159600.
To find the highest common factor of 410,686, 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 686 are 1, 2, 7, 14, 49, 98, 343, 686
The HCF of 410,686 is 2.
Lets's calculate GCF of 410,686
2 | 410, 686 |
205, 343 |
∴ So the GCF of the given numbers is 2 = 2
Now, list down the factors of 410
:1,2,5,10,41,82,205,410
Now, list down the factors of 686
:1,2,7,14,49,98,343,686
Greatest Common Factor
We found the factors 410,686 . The biggest common factor number is the GCF number.
So the greatest common factor 410,686 is 2.
Lets's calculate LCM of 798,400
2 | 798, 400 |
399, 200 |
∴ So the LCM of the given numbers is 2 x 399 x 200 = 159600
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/159600
Therefore, the GCF of Fractions 410/798,686/400 is 2/159600
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 798,400 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(798,400) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(798,400) x common factors =2 x 1 = 2
LCM(798,400) = ( 798 × 400 ) / 2
LCM(798,400) = 319200 / 2
LCM(798,400) = 159600
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 410,686?
The HCF of 410,686 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 410/798, 686/400?
Answer: GCF of Numerators as per given numbers 410/798, 686/400 is
GCF of Numerators i.e. for 410,686 is 2
LCM of denominators i.e. for 798,400 is 159600.
Thus, GCF of Fractions is 2/159600.Finally, GCF of Fractions for 410/798, 686/400 is 2/159600.