GCF of 576/720, 864/861
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 576/720, 864/861 i.e 288/206640 easily. The following is the detailed procedure to determine the greatest common factor of fractions 576/720, 864/861.
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 576/720,864/861?
Given fractions are 576/720,864/861
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 576/720,864/861, numerators are 576,864
Denominators are 720,861
The GCF of 576,864 is 288 .
LCM of 720,861 is 206640.
The greatest common factor of 576/720,864/861 = [GCF of 576,864]/[LCM of 720,861]= 288/206640
Therefore, the GCF of 576/720,864/861 is 288/206640.
To find the highest common factor of 576,864, we have to find the factors of both numbers and list the highest common factor.
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 factors of 864 are 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 27, 32, 36, 48, 54, 72, 96, 108, 144, 216, 288, 432, 864
The HCF of 576,864 is 288.
Lets's calculate GCF of 576,864
| 2 | 576, 864 |
| 2 | 288, 432 |
| 2 | 144, 216 |
| 2 | 72, 108 |
| 2 | 36, 54 |
| 3 | 18, 27 |
| 3 | 6, 9 |
| 2, 3 |
∴ So the GCF of the given numbers is 2 x 2 x 2 x 2 x 2 x 3 x 3 = 288
Greatest Common Factor of 576,864 By Matching Biggest Common Factor Method
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
Now, list down the factors of 864
:1,2,3,4,6,8,9,12,16,18,24,27,32,36,48,54,72,96,108,144,216,288,432,864
Greatest Common Factor
We found the factors 576,864 . The biggest common factor number is the GCF number.
So the greatest common factor 576,864 is 288.
Lets's calculate LCM of 720,861
| 3 | 720, 861 |
| 240, 287 |
∴ So the LCM of the given numbers is 3 x 240 x 287 = 206640
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 288/206640
Therefore, the GCF of Fractions 576/720,864/861 is 288/206640
Least Common Multiple of 720,861 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 720,861 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(720,861) = 3
common factors(in case of two or more numbers have common factors) = 1
GCF(720,861) x common factors =3 x 1 = 3
LCM(720,861) = ( 720 × 861 ) / 3
LCM(720,861) = 619920 / 3
LCM(720,861) = 206640
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FAQs on GCF of Fractions of 576/720, 864/861
1. What is the HCF of 576,864?
The HCF of 576,864 is 288
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 576/720, 864/861?
Answer: GCF of Numerators as per given numbers 576/720, 864/861 is
GCF of Numerators i.e. for 576,864 is 288
LCM of denominators i.e. for 720,861 is 206640.
Thus, GCF of Fractions is 288/206640.Finally, GCF of Fractions for 576/720, 864/861 is 288/206640.