Use our free GCF of Fractions Calculator tool to compute the GCF of 2400/474, 3225/5129 i.e 75/2431146 easily. The following is the detailed procedure to determine the greatest common factor of fractions 2400/474, 3225/5129.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 2400/474,3225/5129
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 2400/474,3225/5129, numerators are 2400,3225
Denominators are 474,5129
The GCF of 2400,3225 is 75 .
LCM of 474,5129 is 2431146.
The greatest common factor of 2400/474,3225/5129 = [GCF of 2400,3225]/[LCM of 474,5129]= 75/2431146
Therefore, the GCF of 2400/474,3225/5129 is 75/2431146.
To find the highest common factor of 2400,3225, we have to find the factors of both numbers and list the highest common factor.
The factors of 2400 are 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 25, 30, 32, 40, 48, 50, 60, 75, 80, 96, 100, 120, 150, 160, 200, 240, 300, 400, 480, 600, 800, 1200, 2400
The factors of 3225 are 1, 3, 5, 15, 25, 43, 75, 129, 215, 645, 1075, 3225
The HCF of 2400,3225 is 75.
Lets's calculate GCF of 2400,3225
3 | 2400, 3225 |
5 | 800, 1075 |
5 | 160, 215 |
32, 43 |
∴ So the GCF of the given numbers is 3 x 5 x 5 = 75
Now, list down the factors of 2400
:1,2,3,4,5,6,8,10,12,15,16,20,24,25,30,32,40,48,50,60,75,80,96,100,120,150,160,200,240,300,400,480,600,800,1200,2400
Now, list down the factors of 3225
:1,3,5,15,25,43,75,129,215,645,1075,3225
Greatest Common Factor
We found the factors 2400,3225 . The biggest common factor number is the GCF number.
So the greatest common factor 2400,3225 is 75.
Lets's calculate LCM of 474,5129
Given numbers has no common factors except 1. So, there LCM is their product i.e 2431146
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 75/2431146
Therefore, the GCF of Fractions 2400/474,3225/5129 is 75/2431146
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 474,5129 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(474,5129) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(474,5129) x common factors =1 x 1 = 1
LCM(474,5129) = ( 474 × 5129 ) / 1
LCM(474,5129) = 2431146 / 1
LCM(474,5129) = 2431146
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 2400,3225?
The HCF of 2400,3225 is 75
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 2400/474, 3225/5129?
Answer: GCF of Numerators as per given numbers 2400/474, 3225/5129 is
GCF of Numerators i.e. for 2400,3225 is 75
LCM of denominators i.e. for 474,5129 is 2431146.
Thus, GCF of Fractions is 75/2431146.Finally, GCF of Fractions for 2400/474, 3225/5129 is 75/2431146.