Use our free GCF of Fractions Calculator tool to compute the GCF of 106/164, 477/616 i.e 53/25256 easily. The following is the detailed procedure to determine the greatest common factor of fractions 106/164, 477/616.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 106/164,477/616
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 106/164,477/616, numerators are 106,477
Denominators are 164,616
The GCF of 106,477 is 53 .
LCM of 164,616 is 25256.
The greatest common factor of 106/164,477/616 = [GCF of 106,477]/[LCM of 164,616]= 53/25256
Therefore, the GCF of 106/164,477/616 is 53/25256.
To find the highest common factor of 106,477, we have to find the factors of both numbers and list the highest common factor.
The factors of 106 are 1, 2, 53, 106
The factors of 477 are 1, 3, 9, 53, 159, 477
The HCF of 106,477 is 53.
Lets's calculate GCF of 106,477
53 | 106, 477 |
2, 9 |
∴ So the GCF of the given numbers is 53 = 53
Now, list down the factors of 106
:1,2,53,106
Now, list down the factors of 477
:1,3,9,53,159,477
Greatest Common Factor
We found the factors 106,477 . The biggest common factor number is the GCF number.
So the greatest common factor 106,477 is 53.
Lets's calculate LCM of 164,616
2 | 164, 616 |
2 | 82, 308 |
41, 154 |
∴ So the LCM of the given numbers is 2 x 2 x 41 x 154 = 25256
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 53/25256
Therefore, the GCF of Fractions 106/164,477/616 is 53/25256
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 164,616 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(164,616) = 4
common factors(in case of two or more numbers have common factors) = 1
GCF(164,616) x common factors =4 x 1 = 4
LCM(164,616) = ( 164 × 616 ) / 4
LCM(164,616) = 101024 / 4
LCM(164,616) = 25256
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 106,477?
The HCF of 106,477 is 53
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 106/164, 477/616?
Answer: GCF of Numerators as per given numbers 106/164, 477/616 is
GCF of Numerators i.e. for 106,477 is 53
LCM of denominators i.e. for 164,616 is 25256.
Thus, GCF of Fractions is 53/25256.Finally, GCF of Fractions for 106/164, 477/616 is 53/25256.