Use our free GCF of Fractions Calculator tool to compute the GCF of 410/319, 694/712 i.e 2/227128 easily. The following is the detailed procedure to determine the greatest common factor of fractions 410/319, 694/712.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 410/319,694/712
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 410/319,694/712, numerators are 410,694
Denominators are 319,712
The GCF of 410,694 is 2 .
LCM of 319,712 is 227128.
The greatest common factor of 410/319,694/712 = [GCF of 410,694]/[LCM of 319,712]= 2/227128
Therefore, the GCF of 410/319,694/712 is 2/227128.
To find the highest common factor of 410,694, 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 694 are 1, 2, 347, 694
The HCF of 410,694 is 2.
Lets's calculate GCF of 410,694
2 | 410, 694 |
205, 347 |
∴ 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 694
:1,2,347,694
Greatest Common Factor
We found the factors 410,694 . The biggest common factor number is the GCF number.
So the greatest common factor 410,694 is 2.
Lets's calculate LCM of 319,712
Given numbers has no common factors except 1. So, there LCM is their product i.e 227128
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/227128
Therefore, the GCF of Fractions 410/319,694/712 is 2/227128
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 319,712 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(319,712) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(319,712) x common factors =1 x 1 = 1
LCM(319,712) = ( 319 × 712 ) / 1
LCM(319,712) = 227128 / 1
LCM(319,712) = 227128
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 410,694?
The HCF of 410,694 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 410/319, 694/712?
Answer: GCF of Numerators as per given numbers 410/319, 694/712 is
GCF of Numerators i.e. for 410,694 is 2
LCM of denominators i.e. for 319,712 is 227128.
Thus, GCF of Fractions is 2/227128.Finally, GCF of Fractions for 410/319, 694/712 is 2/227128.