GCF of 640/39, 576/288
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 640/39, 576/288 i.e 64/3744 easily. The following is the detailed procedure to determine the greatest common factor of fractions 640/39, 576/288.
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 640/39,576/288?
Given fractions are 640/39,576/288
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 640/39,576/288, numerators are 640,576
Denominators are 39,288
The GCF of 640,576 is 64 .
LCM of 39,288 is 3744.
The greatest common factor of 640/39,576/288 = [GCF of 640,576]/[LCM of 39,288]= 64/3744
Therefore, the GCF of 640/39,576/288 is 64/3744.
To find the highest common factor of 640,576, we have to find the factors of both numbers and list the highest common factor.
The factors of 640 are 1, 2, 4, 5, 8, 10, 16, 20, 32, 40, 64, 80, 128, 160, 320, 640
The factors of 576 are 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 32, 36, 48, 64, 72, 96, 144, 192, 288, 576
The HCF of 640,576 is 64.
Lets's calculate GCF of 640,576
| 2 | 640, 576 |
| 2 | 320, 288 |
| 2 | 160, 144 |
| 2 | 80, 72 |
| 2 | 40, 36 |
| 2 | 20, 18 |
| 10, 9 |
∴ So the GCF of the given numbers is 2 x 2 x 2 x 2 x 2 x 2 = 64
Greatest Common Factor of 640,576 By Matching Biggest Common Factor Method
Now, list down the factors of 640
:1,2,4,5,8,10,16,20,32,40,64,80,128,160,320,640
Now, list down the factors of 576
:1,2,3,4,6,8,9,12,16,18,24,32,36,48,64,72,96,144,192,288,576
Greatest Common Factor
We found the factors 640,576 . The biggest common factor number is the GCF number.
So the greatest common factor 640,576 is 64.
Lets's calculate LCM of 39,288
| 3 | 39, 288 |
| 13, 96 |
∴ So the LCM of the given numbers is 3 x 13 x 96 = 3744
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 64/3744
Therefore, the GCF of Fractions 640/39,576/288 is 64/3744
Least Common Multiple of 39,288 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 39,288 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(39,288) = 3
common factors(in case of two or more numbers have common factors) = 1
GCF(39,288) x common factors =3 x 1 = 3
LCM(39,288) = ( 39 × 288 ) / 3
LCM(39,288) = 11232 / 3
LCM(39,288) = 3744
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FAQs on GCF of Fractions of 640/39, 576/288
1. What is the HCF of 640,576?
The HCF of 640,576 is 64
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 640/39, 576/288?
Answer: GCF of Numerators as per given numbers 640/39, 576/288 is
GCF of Numerators i.e. for 640,576 is 64
LCM of denominators i.e. for 39,288 is 3744.
Thus, GCF of Fractions is 64/3744.Finally, GCF of Fractions for 640/39, 576/288 is 64/3744.