GCF of 726/288, 9075/384
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 726/288, 9075/384 i.e 363/1152 easily. The following is the detailed procedure to determine the greatest common factor of fractions 726/288, 9075/384.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
What is the GCF of 726/288,9075/384?
Given fractions are 726/288,9075/384
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 726/288,9075/384, numerators are 726,9075
Denominators are 288,384
The GCF of 726,9075 is 363 .
LCM of 288,384 is 1152.
The greatest common factor of 726/288,9075/384 = [GCF of 726,9075]/[LCM of 288,384]= 363/1152
Therefore, the GCF of 726/288,9075/384 is 363/1152.
To find the highest common factor of 726,9075, we have to find the factors of both numbers and list the highest common factor.
The factors of 726 are 1, 2, 3, 6, 11, 22, 33, 66, 121, 242, 363, 726
The factors of 9075 are 1, 3, 5, 11, 15, 25, 33, 55, 75, 121, 165, 275, 363, 605, 825, 1815, 3025, 9075
The HCF of 726,9075 is 363.
Lets's calculate GCF of 726,9075
| 3 | 726, 9075 |
| 11 | 242, 3025 |
| 11 | 22, 275 |
| 2, 25 |
∴ So the GCF of the given numbers is 3 x 11 x 11 = 363
Greatest Common Factor of 726,9075 By Matching Biggest Common Factor Method
Now, list down the factors of 726
:1,2,3,6,11,22,33,66,121,242,363,726
Now, list down the factors of 9075
:1,3,5,11,15,25,33,55,75,121,165,275,363,605,825,1815,3025,9075
Greatest Common Factor
We found the factors 726,9075 . The biggest common factor number is the GCF number.
So the greatest common factor 726,9075 is 363.
Lets's calculate LCM of 288,384
| 2 | 288, 384 |
| 2 | 144, 192 |
| 2 | 72, 96 |
| 2 | 36, 48 |
| 2 | 18, 24 |
| 3 | 9, 12 |
| 3, 4 |
∴ So the LCM of the given numbers is 2 x 2 x 2 x 2 x 2 x 3 x 3 x 4 = 1152
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 363/1152
Therefore, the GCF of Fractions 726/288,9075/384 is 363/1152
Least Common Multiple of 288,384 with GCF Formula
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 288,384 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(288,384) = 96
common factors(in case of two or more numbers have common factors) = 1
GCF(288,384) x common factors =96 x 1 = 96
LCM(288,384) = ( 288 × 384 ) / 96
LCM(288,384) = 110592 / 96
LCM(288,384) = 1152
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FAQs on GCF of Fractions of 726/288, 9075/384
1. What is the HCF of 726,9075?
The HCF of 726,9075 is 363
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 726/288, 9075/384?
Answer: GCF of Numerators as per given numbers 726/288, 9075/384 is
GCF of Numerators i.e. for 726,9075 is 363
LCM of denominators i.e. for 288,384 is 1152.
Thus, GCF of Fractions is 363/1152.Finally, GCF of Fractions for 726/288, 9075/384 is 363/1152.