Use our free GCF of Fractions Calculator tool to compute the GCF of 645/678, 6489/2493 i.e 3/563418 easily. The following is the detailed procedure to determine the greatest common factor of fractions 645/678, 6489/2493.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 645/678,6489/2493
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 645/678,6489/2493, numerators are 645,6489
Denominators are 678,2493
The GCF of 645,6489 is 3 .
LCM of 678,2493 is 563418.
The greatest common factor of 645/678,6489/2493 = [GCF of 645,6489]/[LCM of 678,2493]= 3/563418
Therefore, the GCF of 645/678,6489/2493 is 3/563418.
To find the highest common factor of 645,6489, we have to find the factors of both numbers and list the highest common factor.
The factors of 645 are 1, 3, 5, 15, 43, 129, 215, 645
The factors of 6489 are 1, 3, 7, 9, 21, 63, 103, 309, 721, 927, 2163, 6489
The HCF of 645,6489 is 3.
Lets's calculate GCF of 645,6489
3 | 645, 6489 |
215, 2163 |
∴ So the GCF of the given numbers is 3 = 3
Now, list down the factors of 645
:1,3,5,15,43,129,215,645
Now, list down the factors of 6489
:1,3,7,9,21,63,103,309,721,927,2163,6489
Greatest Common Factor
We found the factors 645,6489 . The biggest common factor number is the GCF number.
So the greatest common factor 645,6489 is 3.
Lets's calculate LCM of 678,2493
3 | 678, 2493 |
226, 831 |
∴ So the LCM of the given numbers is 3 x 226 x 831 = 563418
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 3/563418
Therefore, the GCF of Fractions 645/678,6489/2493 is 3/563418
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 678,2493 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(678,2493) = 3
common factors(in case of two or more numbers have common factors) = 1
GCF(678,2493) x common factors =3 x 1 = 3
LCM(678,2493) = ( 678 × 2493 ) / 3
LCM(678,2493) = 1690254 / 3
LCM(678,2493) = 563418
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 645,6489?
The HCF of 645,6489 is 3
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 645/678, 6489/2493?
Answer: GCF of Numerators as per given numbers 645/678, 6489/2493 is
GCF of Numerators i.e. for 645,6489 is 3
LCM of denominators i.e. for 678,2493 is 563418.
Thus, GCF of Fractions is 3/563418.Finally, GCF of Fractions for 645/678, 6489/2493 is 3/563418.