Use our free GCF of Fractions Calculator tool to compute the GCF of 7368/589, 6420/5187 i.e 12/160797 easily. The following is the detailed procedure to determine the greatest common factor of fractions 7368/589, 6420/5187.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 7368/589,6420/5187
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 7368/589,6420/5187, numerators are 7368,6420
Denominators are 589,5187
The GCF of 7368,6420 is 12 .
LCM of 589,5187 is 160797.
The greatest common factor of 7368/589,6420/5187 = [GCF of 7368,6420]/[LCM of 589,5187]= 12/160797
Therefore, the GCF of 7368/589,6420/5187 is 12/160797.
To find the highest common factor of 7368,6420, we have to find the factors of both numbers and list the highest common factor.
The factors of 7368 are 1, 2, 3, 4, 6, 8, 12, 24, 307, 614, 921, 1228, 1842, 2456, 3684, 7368
The factors of 6420 are 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60, 107, 214, 321, 428, 535, 642, 1070, 1284, 1605, 2140, 3210, 6420
The HCF of 7368,6420 is 12.
Lets's calculate GCF of 7368,6420
2 | 7368, 6420 |
2 | 3684, 3210 |
3 | 1842, 1605 |
614, 535 |
∴ So the GCF of the given numbers is 2 x 2 x 3 = 12
Now, list down the factors of 7368
:1,2,3,4,6,8,12,24,307,614,921,1228,1842,2456,3684,7368
Now, list down the factors of 6420
:1,2,3,4,5,6,10,12,15,20,30,60,107,214,321,428,535,642,1070,1284,1605,2140,3210,6420
Greatest Common Factor
We found the factors 7368,6420 . The biggest common factor number is the GCF number.
So the greatest common factor 7368,6420 is 12.
Lets's calculate LCM of 589,5187
19 | 589, 5187 |
31, 273 |
∴ So the LCM of the given numbers is 19 x 31 x 273 = 160797
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 12/160797
Therefore, the GCF of Fractions 7368/589,6420/5187 is 12/160797
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 589,5187 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(589,5187) = 19
common factors(in case of two or more numbers have common factors) = 1
GCF(589,5187) x common factors =19 x 1 = 19
LCM(589,5187) = ( 589 × 5187 ) / 19
LCM(589,5187) = 3055143 / 19
LCM(589,5187) = 160797
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 7368,6420?
The HCF of 7368,6420 is 12
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 7368/589, 6420/5187?
Answer: GCF of Numerators as per given numbers 7368/589, 6420/5187 is
GCF of Numerators i.e. for 7368,6420 is 12
LCM of denominators i.e. for 589,5187 is 160797.
Thus, GCF of Fractions is 12/160797.Finally, GCF of Fractions for 7368/589, 6420/5187 is 12/160797.