Use our free GCF of Fractions Calculator tool to compute the GCF of 384/203, 480/914 i.e 96/185542 easily. The following is the detailed procedure to determine the greatest common factor of fractions 384/203, 480/914.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 384/203,480/914
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 384/203,480/914, numerators are 384,480
Denominators are 203,914
The GCF of 384,480 is 96 .
LCM of 203,914 is 185542.
The greatest common factor of 384/203,480/914 = [GCF of 384,480]/[LCM of 203,914]= 96/185542
Therefore, the GCF of 384/203,480/914 is 96/185542.
To find the highest common factor of 384,480, 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 480 are 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 32, 40, 48, 60, 80, 96, 120, 160, 240, 480
The HCF of 384,480 is 96.
Lets's calculate GCF of 384,480
2 | 384, 480 |
2 | 192, 240 |
2 | 96, 120 |
2 | 48, 60 |
2 | 24, 30 |
3 | 12, 15 |
4, 5 |
∴ So the GCF of the given numbers is 2 x 2 x 2 x 2 x 2 x 3 = 96
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 480
:1,2,3,4,5,6,8,10,12,15,16,20,24,30,32,40,48,60,80,96,120,160,240,480
Greatest Common Factor
We found the factors 384,480 . The biggest common factor number is the GCF number.
So the greatest common factor 384,480 is 96.
Lets's calculate LCM of 203,914
Given numbers has no common factors except 1. So, there LCM is their product i.e 185542
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 96/185542
Therefore, the GCF of Fractions 384/203,480/914 is 96/185542
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 203,914 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(203,914) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(203,914) x common factors =1 x 1 = 1
LCM(203,914) = ( 203 × 914 ) / 1
LCM(203,914) = 185542 / 1
LCM(203,914) = 185542
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 384,480?
The HCF of 384,480 is 96
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 384/203, 480/914?
Answer: GCF of Numerators as per given numbers 384/203, 480/914 is
GCF of Numerators i.e. for 384,480 is 96
LCM of denominators i.e. for 203,914 is 185542.
Thus, GCF of Fractions is 96/185542.Finally, GCF of Fractions for 384/203, 480/914 is 96/185542.