Use our free GCF of Fractions Calculator tool to compute the GCF of 629/196, 986/105 i.e 17/2940 easily. The following is the detailed procedure to determine the greatest common factor of fractions 629/196, 986/105.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 629/196,986/105
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 629/196,986/105, numerators are 629,986
Denominators are 196,105
The GCF of 629,986 is 17 .
LCM of 196,105 is 2940.
The greatest common factor of 629/196,986/105 = [GCF of 629,986]/[LCM of 196,105]= 17/2940
Therefore, the GCF of 629/196,986/105 is 17/2940.
To find the highest common factor of 629,986, we have to find the factors of both numbers and list the highest common factor.
The factors of 629 are 1, 17, 37, 629
The factors of 986 are 1, 2, 17, 29, 34, 58, 493, 986
The HCF of 629,986 is 17.
Lets's calculate GCF of 629,986
17 | 629, 986 |
37, 58 |
∴ So the GCF of the given numbers is 17 = 17
Now, list down the factors of 629
:1,17,37,629
Now, list down the factors of 986
:1,2,17,29,34,58,493,986
Greatest Common Factor
We found the factors 629,986 . The biggest common factor number is the GCF number.
So the greatest common factor 629,986 is 17.
Lets's calculate LCM of 196,105
7 | 196, 105 |
28, 15 |
∴ So the LCM of the given numbers is 7 x 28 x 15 = 2940
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 17/2940
Therefore, the GCF of Fractions 629/196,986/105 is 17/2940
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 196,105 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(196,105) = 7
common factors(in case of two or more numbers have common factors) = 1
GCF(196,105) x common factors =7 x 1 = 7
LCM(196,105) = ( 196 × 105 ) / 7
LCM(196,105) = 20580 / 7
LCM(196,105) = 2940
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 629,986?
The HCF of 629,986 is 17
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 629/196, 986/105?
Answer: GCF of Numerators as per given numbers 629/196, 986/105 is
GCF of Numerators i.e. for 629,986 is 17
LCM of denominators i.e. for 196,105 is 2940.
Thus, GCF of Fractions is 17/2940.Finally, GCF of Fractions for 629/196, 986/105 is 17/2940.