Use our free GCF of Fractions Calculator tool to compute the GCF of 105/888, 225/102 i.e 15/15096 easily. The following is the detailed procedure to determine the greatest common factor of fractions 105/888, 225/102.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 105/888,225/102
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 105/888,225/102, numerators are 105,225
Denominators are 888,102
The GCF of 105,225 is 15 .
LCM of 888,102 is 15096.
The greatest common factor of 105/888,225/102 = [GCF of 105,225]/[LCM of 888,102]= 15/15096
Therefore, the GCF of 105/888,225/102 is 15/15096.
To find the highest common factor of 105,225, we have to find the factors of both numbers and list the highest common factor.
The factors of 105 are 1, 3, 5, 7, 15, 21, 35, 105
The factors of 225 are 1, 3, 5, 9, 15, 25, 45, 75, 225
The HCF of 105,225 is 15.
Lets's calculate GCF of 105,225
3 | 105, 225 |
5 | 35, 75 |
7, 15 |
∴ So the GCF of the given numbers is 3 x 5 = 15
Now, list down the factors of 105
:1,3,5,7,15,21,35,105
Now, list down the factors of 225
:1,3,5,9,15,25,45,75,225
Greatest Common Factor
We found the factors 105,225 . The biggest common factor number is the GCF number.
So the greatest common factor 105,225 is 15.
Lets's calculate LCM of 888,102
2 | 888, 102 |
3 | 444, 51 |
148, 17 |
∴ So the LCM of the given numbers is 2 x 3 x 148 x 17 = 15096
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 15/15096
Therefore, the GCF of Fractions 105/888,225/102 is 15/15096
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 888,102 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(888,102) = 6
common factors(in case of two or more numbers have common factors) = 1
GCF(888,102) x common factors =6 x 1 = 6
LCM(888,102) = ( 888 × 102 ) / 6
LCM(888,102) = 90576 / 6
LCM(888,102) = 15096
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 105,225?
The HCF of 105,225 is 15
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 105/888, 225/102?
Answer: GCF of Numerators as per given numbers 105/888, 225/102 is
GCF of Numerators i.e. for 105,225 is 15
LCM of denominators i.e. for 888,102 is 15096.
Thus, GCF of Fractions is 15/15096.Finally, GCF of Fractions for 105/888, 225/102 is 15/15096.