Use our free GCF of Fractions Calculator tool to compute the GCF of 628/840, 198/315 i.e 2/2520 easily. The following is the detailed procedure to determine the greatest common factor of fractions 628/840, 198/315.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 628/840,198/315
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 628/840,198/315, numerators are 628,198
Denominators are 840,315
The GCF of 628,198 is 2 .
LCM of 840,315 is 2520.
The greatest common factor of 628/840,198/315 = [GCF of 628,198]/[LCM of 840,315]= 2/2520
Therefore, the GCF of 628/840,198/315 is 2/2520.
To find the highest common factor of 628,198, we have to find the factors of both numbers and list the highest common factor.
The factors of 628 are 1, 2, 4, 157, 314, 628
The factors of 198 are 1, 2, 3, 6, 9, 11, 18, 22, 33, 66, 99, 198
The HCF of 628,198 is 2.
Lets's calculate GCF of 628,198
2 | 628, 198 |
314, 99 |
∴ So the GCF of the given numbers is 2 = 2
Now, list down the factors of 628
:1,2,4,157,314,628
Now, list down the factors of 198
:1,2,3,6,9,11,18,22,33,66,99,198
Greatest Common Factor
We found the factors 628,198 . The biggest common factor number is the GCF number.
So the greatest common factor 628,198 is 2.
Lets's calculate LCM of 840,315
3 | 840, 315 |
5 | 280, 105 |
7 | 56, 21 |
8, 3 |
∴ So the LCM of the given numbers is 3 x 5 x 7 x 8 x 3 = 2520
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/2520
Therefore, the GCF of Fractions 628/840,198/315 is 2/2520
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 840,315 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(840,315) = 105
common factors(in case of two or more numbers have common factors) = 1
GCF(840,315) x common factors =105 x 1 = 105
LCM(840,315) = ( 840 × 315 ) / 105
LCM(840,315) = 264600 / 105
LCM(840,315) = 2520
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 628,198?
The HCF of 628,198 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 628/840, 198/315?
Answer: GCF of Numerators as per given numbers 628/840, 198/315 is
GCF of Numerators i.e. for 628,198 is 2
LCM of denominators i.e. for 840,315 is 2520.
Thus, GCF of Fractions is 2/2520.Finally, GCF of Fractions for 628/840, 198/315 is 2/2520.