Use our free GCF of Fractions Calculator tool to compute the GCF of 750/405, 288/735 i.e 6/19845 easily. The following is the detailed procedure to determine the greatest common factor of fractions 750/405, 288/735.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 750/405,288/735
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 750/405,288/735, numerators are 750,288
Denominators are 405,735
The GCF of 750,288 is 6 .
LCM of 405,735 is 19845.
The greatest common factor of 750/405,288/735 = [GCF of 750,288]/[LCM of 405,735]= 6/19845
Therefore, the GCF of 750/405,288/735 is 6/19845.
To find the highest common factor of 750,288, we have to find the factors of both numbers and list the highest common factor.
The factors of 750 are 1, 2, 3, 5, 6, 10, 15, 25, 30, 50, 75, 125, 150, 250, 375, 750
The factors of 288 are 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 32, 36, 48, 72, 96, 144, 288
The HCF of 750,288 is 6.
Lets's calculate GCF of 750,288
2 | 750, 288 |
3 | 375, 144 |
125, 48 |
∴ So the GCF of the given numbers is 2 x 3 = 6
Now, list down the factors of 750
:1,2,3,5,6,10,15,25,30,50,75,125,150,250,375,750
Now, list down the factors of 288
:1,2,3,4,6,8,9,12,16,18,24,32,36,48,72,96,144,288
Greatest Common Factor
We found the factors 750,288 . The biggest common factor number is the GCF number.
So the greatest common factor 750,288 is 6.
Lets's calculate LCM of 405,735
3 | 405, 735 |
5 | 135, 245 |
27, 49 |
∴ So the LCM of the given numbers is 3 x 5 x 27 x 49 = 19845
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 6/19845
Therefore, the GCF of Fractions 750/405,288/735 is 6/19845
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 405,735 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(405,735) = 15
common factors(in case of two or more numbers have common factors) = 1
GCF(405,735) x common factors =15 x 1 = 15
LCM(405,735) = ( 405 × 735 ) / 15
LCM(405,735) = 297675 / 15
LCM(405,735) = 19845
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 750,288?
The HCF of 750,288 is 6
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 750/405, 288/735?
Answer: GCF of Numerators as per given numbers 750/405, 288/735 is
GCF of Numerators i.e. for 750,288 is 6
LCM of denominators i.e. for 405,735 is 19845.
Thus, GCF of Fractions is 6/19845.Finally, GCF of Fractions for 750/405, 288/735 is 6/19845.