The number 576
576 is a perfect square (24²). Its prime factorisation is × . Divisors (21): 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 32, 36, 48, 64, 72 … 576.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 576: a perfect square (24²); a Harshad number: divisible by its digit sum 18.
- 2
576 is composite. Its prime factorisation is
- 3
The divisors add up to 1651; without 576 itself that is 1075, so 576 is abundant (1075 is more than 576). Euler's totient φ(576) = 192 numbers up to 576 share no factor with it.
- 4
The digits of 576 add up to 18, and repeating that until one digit is left gives the digital root 9. The Collatz sequence (halve if even, else 3n+1) takes 25 steps to reach 1.
LaTeX source of the formulas on this page
\[ 576 = 2^{6} \times 3^{2} \]576 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 21 |
| Sum of divisors | 1651 |
| Euler totient φ(n) | 192 |
| Square | 331776 |
| Cube | 191102976 |
| Square root | 24 |
| Digit sum / digital root | 18 / 9 |
| Collatz steps to 1 | 25 |
| Scientific notation | 5.76 × |
| Perfect power |
576 in other forms
| Form | Value |
|---|---|
| In words | five hundred and seventy-six |
| Roman numerals | DLXXVI |
| Binary (base 2) | 1001000000 |
| Octal (base 8) | 1100 |
| Hexadecimal (base 16) | 240 |
| Base 3 | 210100 |
| As time | 576 seconds = 9 min 36 s |
Is 576 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (576 ÷ 2 = 288) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (576 ÷ 3 = 192) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (576 ÷ 4 = 144) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | No (remainder 1) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (576 ÷ 6 = 96) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 2) | A number is divisible by 7 if double the last digit and subtract it from the rest: the result is a multiple of 7. |
| 8 | Yes (576 ÷ 8 = 72) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | Yes (576 ÷ 9 = 64) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | No (remainder 6) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 4) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (576 ÷ 12 = 48) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 576 a prime number?
No. 576 = × , so it is divisible by 2.
What are 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.
What is 576 in binary?
1001000000 (hexadecimal 240, octal 1100).
What is the square root of 576?
24, because 24 × 24 = 576.
What is 576 in Roman numerals?
DLXXVI.
Is 576 divisible by 3?
Yes. Its digits add up to 18, a multiple of 3.
What is special about the number 576?
576 is a perfect square (24²); a Harshad number: divisible by its digit sum 18.