Use our free GCF of Fractions Calculator tool to compute the GCF of 384/121, 225/209 i.e 3/2299 easily. The following is the detailed procedure to determine the greatest common factor of fractions 384/121, 225/209.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 384/121,225/209
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 384/121,225/209, numerators are 384,225
Denominators are 121,209
The GCF of 384,225 is 3 .
LCM of 121,209 is 2299.
The greatest common factor of 384/121,225/209 = [GCF of 384,225]/[LCM of 121,209]= 3/2299
Therefore, the GCF of 384/121,225/209 is 3/2299.
To find the highest common factor of 384,225, we have to find the factors of both numbers and list the highest common factor.
The factors of 384 are 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 64, 96, 128, 192, 384
The factors of 225 are 1, 3, 5, 9, 15, 25, 45, 75, 225
The HCF of 384,225 is 3.
Lets's calculate GCF of 384,225
3 | 384, 225 |
128, 75 |
∴ So the GCF of the given numbers is 3 = 3
Now, list down the factors of 384
:1,2,3,4,6,8,12,16,24,32,48,64,96,128,192,384
Now, list down the factors of 225
:1,3,5,9,15,25,45,75,225
Greatest Common Factor
We found the factors 384,225 . The biggest common factor number is the GCF number.
So the greatest common factor 384,225 is 3.
Lets's calculate LCM of 121,209
11 | 121, 209 |
11, 19 |
∴ So the LCM of the given numbers is 11 x 11 x 19 = 2299
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 3/2299
Therefore, the GCF of Fractions 384/121,225/209 is 3/2299
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 121,209 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(121,209) = 11
common factors(in case of two or more numbers have common factors) = 1
GCF(121,209) x common factors =11 x 1 = 11
LCM(121,209) = ( 121 × 209 ) / 11
LCM(121,209) = 25289 / 11
LCM(121,209) = 2299
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 384,225?
The HCF of 384,225 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 384/121, 225/209?
Answer: GCF of Numerators as per given numbers 384/121, 225/209 is
GCF of Numerators i.e. for 384,225 is 3
LCM of denominators i.e. for 121,209 is 2299.
Thus, GCF of Fractions is 3/2299.Finally, GCF of Fractions for 384/121, 225/209 is 3/2299.