Use our free GCF of Fractions Calculator tool to compute the GCF of 462/102, 231/511 i.e 231/52122 easily. The following is the detailed procedure to determine the greatest common factor of fractions 462/102, 231/511.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 462/102,231/511
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 462/102,231/511, numerators are 462,231
Denominators are 102,511
The GCF of 462,231 is 231 .
LCM of 102,511 is 52122.
The greatest common factor of 462/102,231/511 = [GCF of 462,231]/[LCM of 102,511]= 231/52122
Therefore, the GCF of 462/102,231/511 is 231/52122.
To find the highest common factor of 462,231, we have to find the factors of both numbers and list the highest common factor.
The factors of 462 are 1, 2, 3, 6, 7, 11, 14, 21, 22, 33, 42, 66, 77, 154, 231, 462
The factors of 231 are 1, 3, 7, 11, 21, 33, 77, 231
The HCF of 462,231 is 231.
Lets's calculate GCF of 462,231
3 | 462, 231 |
7 | 154, 77 |
11 | 22, 11 |
2, 1 |
∴ So the GCF of the given numbers is 3 x 7 x 11 = 231
Now, list down the factors of 462
:1,2,3,6,7,11,14,21,22,33,42,66,77,154,231,462
Now, list down the factors of 231
:1,3,7,11,21,33,77,231
Greatest Common Factor
We found the factors 462,231 . The biggest common factor number is the GCF number.
So the greatest common factor 462,231 is 231.
Lets's calculate LCM of 102,511
Given numbers has no common factors except 1. So, there LCM is their product i.e 52122
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 231/52122
Therefore, the GCF of Fractions 462/102,231/511 is 231/52122
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 102,511 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(102,511) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(102,511) x common factors =1 x 1 = 1
LCM(102,511) = ( 102 × 511 ) / 1
LCM(102,511) = 52122 / 1
LCM(102,511) = 52122
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 462,231?
The HCF of 462,231 is 231
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 462/102, 231/511?
Answer: GCF of Numerators as per given numbers 462/102, 231/511 is
GCF of Numerators i.e. for 462,231 is 231
LCM of denominators i.e. for 102,511 is 52122.
Thus, GCF of Fractions is 231/52122.Finally, GCF of Fractions for 462/102, 231/511 is 231/52122.