Use our free GCF of Fractions Calculator tool to compute the GCF of 96/53, 123/10, 405/215 i.e 3/22790 easily. The following is the detailed procedure to determine the greatest common factor of fractions 96/53, 123/10, 405/215.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 96/53,123/10,405/215
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 96/53,123/10,405/215, numerators are 96,123,405
Denominators are 53,10,215
The GCF of 96,123,405 is 3 .
LCM of 53,10,215 is 22790.
The greatest common factor of 96/53,123/10,405/215 = [GCF of 96,123,405]/[LCM of 53,10,215]= 3/22790
Therefore, the GCF of 96/53,123/10,405/215 is 3/22790.
To find the highest common factor of 96,123,405, we have to find the factors of both numbers and list the highest common factor.
The factors of 96 are 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 96
The factors of 123 are 1, 3, 41, 123
The factors of 405 are 1, 3, 5, 9, 15, 27, 45, 81, 135, 405
The HCF of 96,123,405 is 3.
Lets's calculate GCF of 96,123,405
3 | 96, 123, 405 |
32, 41, 135 |
∴ So the GCF of the given numbers is 3 = 3
Now, list down the factors of 96
:1,2,3,4,6,8,12,16,24,32,48,96
Now, list down the factors of 123
:1,3,41,123
Now, list down the factors of 405
:1,3,5,9,15,27,45,81,135,405
Greatest Common Factor
We found the factors 96,123,405 . The biggest common factor number is the GCF number.
So the greatest common factor 96,123,405 is 3.
Lets's calculate LCM of 53,10,215
5 | 53, 10, 215 |
53, 2, 43 |
∴ So the LCM of the given numbers is 5 x 53 x 2 x 43 = 22790
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 3/22790
Therefore, the GCF of Fractions 96/53,123/10,405/215 is 3/22790
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 53,10,215 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(53,10,215) = 1
common factors(in case of two or more numbers have common factors) = 5
GCF(53,10,215) x common factors =1 x 5 = 5
LCM(53,10,215) = ( 53 × 10 × 215 ) / 5
LCM(53,10,215) = 113950 / 5
LCM(53,10,215) = 22790
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 96,123,405?
The HCF of 96,123,405 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 96/53, 123/10, 405/215?
Answer: GCF of Numerators as per given numbers 96/53, 123/10, 405/215 is
GCF of Numerators i.e. for 96,123,405 is 3
LCM of denominators i.e. for 53,10,215 is 22790.
Thus, GCF of Fractions is 3/22790.Finally, GCF of Fractions for 96/53, 123/10, 405/215 is 3/22790.