The number 23040
23040 is a composite number with 60 divisors. Its prime factorisation is × × 5. Divisors (60): 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 16, 18, 20, 24, 30 … 23040.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 23040: a Harshad number: divisible by its digit sum 9.
- 2
23040 is composite. Its prime factorisation is
- 3
The divisors add up to 79794; without 23040 itself that is 56754, so 23040 is abundant (56754 is more than 23040). Euler's totient φ(23040) = 6144 numbers up to 23040 share no factor with it.
- 4
The digits of 23040 add up to 9, 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
\[ 23040 = 2^{9} \times 3^{2} \times 5 \]23040 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 60 |
| Sum of divisors | 79794 |
| Euler totient φ(n) | 6144 |
| Square | 530841600 |
| Cube | 12230590464000 |
| Square root | 151.789328 (= 48√10) |
| Digit sum / digital root | 9 / 9 |
| Collatz steps to 1 | 25 |
| Scientific notation | 2.304 × |
23040 in other forms
| Form | Value |
|---|---|
| In words | twenty-three thousand and forty |
| Binary (base 2) | 101101000000000 |
| Octal (base 8) | 55000 |
| Hexadecimal (base 16) | 5A00 |
| Base 3 | 1011121100 |
| As time | 23040 seconds = 6 h 24 min 0 s |
Is 23040 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (23040 ÷ 2 = 11520) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (23040 ÷ 3 = 7680) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (23040 ÷ 4 = 5760) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | Yes (23040 ÷ 5 = 4608) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (23040 ÷ 6 = 3840) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 3) | 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 (23040 ÷ 8 = 2880) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | Yes (23040 ÷ 9 = 2560) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | Yes (23040 ÷ 10 = 2304) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 6) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (23040 ÷ 12 = 1920) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 23040 a prime number?
No. 23040 = × × 5, so it is divisible by 2.
What are the factors of 23040?
1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 16, 18, 20, 24, 30, 32, 36, 40, 45, 48, 60, 64, 72, 80, 90, 96, 120, 128, 144, 160, 180, 192, 240, 256, 288, 320, 360, 384, 480, 512, 576, 640, 720, 768, 960, 1152, 1280, 1440, 1536, 1920, 2304, 2560, 2880, 3840, 4608, 5760, 7680, 11520, 23040.
What is 23040 in binary?
101101000000000 (hexadecimal 5A00, octal 55000).
What is the square root of 23040?
About 151.7893, exactly 48√10.
Is 23040 divisible by 3?
Yes. Its digits add up to 9, a multiple of 3.
What is special about the number 23040?
23040 is a Harshad number: divisible by its digit sum 9.