Use our free GCF of Fractions Calculator tool to compute the GCF of 390/205, 8614/928 i.e 2/190240 easily. The following is the detailed procedure to determine the greatest common factor of fractions 390/205, 8614/928.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 390/205,8614/928
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 390/205,8614/928, numerators are 390,8614
Denominators are 205,928
The GCF of 390,8614 is 2 .
LCM of 205,928 is 190240.
The greatest common factor of 390/205,8614/928 = [GCF of 390,8614]/[LCM of 205,928]= 2/190240
Therefore, the GCF of 390/205,8614/928 is 2/190240.
To find the highest common factor of 390,8614, we have to find the factors of both numbers and list the highest common factor.
The factors of 390 are 1, 2, 3, 5, 6, 10, 13, 15, 26, 30, 39, 65, 78, 130, 195, 390
The factors of 8614 are 1, 2, 59, 73, 118, 146, 4307, 8614
The HCF of 390,8614 is 2.
Lets's calculate GCF of 390,8614
2 | 390, 8614 |
195, 4307 |
∴ So the GCF of the given numbers is 2 = 2
Now, list down the factors of 390
:1,2,3,5,6,10,13,15,26,30,39,65,78,130,195,390
Now, list down the factors of 8614
:1,2,59,73,118,146,4307,8614
Greatest Common Factor
We found the factors 390,8614 . The biggest common factor number is the GCF number.
So the greatest common factor 390,8614 is 2.
Lets's calculate LCM of 205,928
Given numbers has no common factors except 1. So, there LCM is their product i.e 190240
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/190240
Therefore, the GCF of Fractions 390/205,8614/928 is 2/190240
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 205,928 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(205,928) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(205,928) x common factors =1 x 1 = 1
LCM(205,928) = ( 205 × 928 ) / 1
LCM(205,928) = 190240 / 1
LCM(205,928) = 190240
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 390,8614?
The HCF of 390,8614 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 390/205, 8614/928?
Answer: GCF of Numerators as per given numbers 390/205, 8614/928 is
GCF of Numerators i.e. for 390,8614 is 2
LCM of denominators i.e. for 205,928 is 190240.
Thus, GCF of Fractions is 2/190240.Finally, GCF of Fractions for 390/205, 8614/928 is 2/190240.