Use our free GCF of Fractions Calculator tool to compute the GCF of 878/269, 310/774 i.e 2/208206 easily. The following is the detailed procedure to determine the greatest common factor of fractions 878/269, 310/774.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 878/269,310/774
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 878/269,310/774, numerators are 878,310
Denominators are 269,774
The GCF of 878,310 is 2 .
LCM of 269,774 is 208206.
The greatest common factor of 878/269,310/774 = [GCF of 878,310]/[LCM of 269,774]= 2/208206
Therefore, the GCF of 878/269,310/774 is 2/208206.
To find the highest common factor of 878,310, 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 310 are 1, 2, 5, 10, 31, 62, 155, 310
The HCF of 878,310 is 2.
Lets's calculate GCF of 878,310
2 | 878, 310 |
439, 155 |
∴ 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 310
:1,2,5,10,31,62,155,310
Greatest Common Factor
We found the factors 878,310 . The biggest common factor number is the GCF number.
So the greatest common factor 878,310 is 2.
Lets's calculate LCM of 269,774
Given numbers has no common factors except 1. So, there LCM is their product i.e 208206
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/208206
Therefore, the GCF of Fractions 878/269,310/774 is 2/208206
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 269,774 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(269,774) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(269,774) x common factors =1 x 1 = 1
LCM(269,774) = ( 269 × 774 ) / 1
LCM(269,774) = 208206 / 1
LCM(269,774) = 208206
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 878,310?
The HCF of 878,310 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 878/269, 310/774?
Answer: GCF of Numerators as per given numbers 878/269, 310/774 is
GCF of Numerators i.e. for 878,310 is 2
LCM of denominators i.e. for 269,774 is 208206.
Thus, GCF of Fractions is 2/208206.Finally, GCF of Fractions for 878/269, 310/774 is 2/208206.