Use our free GCF of Fractions Calculator tool to compute the GCF of 878/777, 782/409 i.e 2/317793 easily. The following is the detailed procedure to determine the greatest common factor of fractions 878/777, 782/409.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 878/777,782/409
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 878/777,782/409, numerators are 878,782
Denominators are 777,409
The GCF of 878,782 is 2 .
LCM of 777,409 is 317793.
The greatest common factor of 878/777,782/409 = [GCF of 878,782]/[LCM of 777,409]= 2/317793
Therefore, the GCF of 878/777,782/409 is 2/317793.
To find the highest common factor of 878,782, we have to find the factors of both numbers and list the highest common factor.
The factors of 878 are 1, 2, 439, 878
The factors of 782 are 1, 2, 17, 23, 34, 46, 391, 782
The HCF of 878,782 is 2.
Lets's calculate GCF of 878,782
2 | 878, 782 |
439, 391 |
∴ So the GCF of the given numbers is 2 = 2
Now, list down the factors of 878
:1,2,439,878
Now, list down the factors of 782
:1,2,17,23,34,46,391,782
Greatest Common Factor
We found the factors 878,782 . The biggest common factor number is the GCF number.
So the greatest common factor 878,782 is 2.
Lets's calculate LCM of 777,409
Given numbers has no common factors except 1. So, there LCM is their product i.e 317793
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/317793
Therefore, the GCF of Fractions 878/777,782/409 is 2/317793
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 777,409 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(777,409) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(777,409) x common factors =1 x 1 = 1
LCM(777,409) = ( 777 × 409 ) / 1
LCM(777,409) = 317793 / 1
LCM(777,409) = 317793
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 878,782?
The HCF of 878,782 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 878/777, 782/409?
Answer: GCF of Numerators as per given numbers 878/777, 782/409 is
GCF of Numerators i.e. for 878,782 is 2
LCM of denominators i.e. for 777,409 is 317793.
Thus, GCF of Fractions is 2/317793.Finally, GCF of Fractions for 878/777, 782/409 is 2/317793.