The number 11520
11520 is a composite number with 54 divisors. Its prime factorisation is × × 5. Divisors (54): 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 16, 18, 20, 24, 30 … 11520.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 11520: a happy number: repeatedly adding the squares of its digits reaches 1; a Harshad number: divisible by its digit sum 9.
- 2
11520 is composite. Its prime factorisation is
- 3
The divisors add up to 39858; without 11520 itself that is 28338, so 11520 is abundant (28338 is more than 11520). Euler's totient φ(11520) = 3072 numbers up to 11520 share no factor with it.
- 4
The digits of 11520 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 24 steps to reach 1.
LaTeX source of the formulas on this page
\[ 11520 = 2^{8} \times 3^{2} \times 5 \]11520 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 54 |
| Sum of divisors | 39858 |
| Euler totient φ(n) | 3072 |
| Square | 132710400 |
| Cube | 1528823808000 |
| Square root | 107.331263 (= 48√5) |
| Digit sum / digital root | 9 / 9 |
| Collatz steps to 1 | 24 |
| Scientific notation | 1.152 × |
11520 in other forms
| Form | Value |
|---|---|
| In words | eleven thousand five hundred and twenty |
| Binary (base 2) | 10110100000000 |
| Octal (base 8) | 26400 |
| Hexadecimal (base 16) | 2D00 |
| Base 3 | 120210200 |
| As time | 11520 seconds = 3 h 12 min 0 s |
Is 11520 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (11520 ÷ 2 = 5760) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (11520 ÷ 3 = 3840) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (11520 ÷ 4 = 2880) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | Yes (11520 ÷ 5 = 2304) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (11520 ÷ 6 = 1920) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 5) | 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 (11520 ÷ 8 = 1440) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | Yes (11520 ÷ 9 = 1280) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | Yes (11520 ÷ 10 = 1152) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 3) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (11520 ÷ 12 = 960) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 11520 a prime number?
No. 11520 = × × 5, so it is divisible by 2.
What are the factors of 11520?
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, 576, 640, 720, 768, 960, 1152, 1280, 1440, 1920, 2304, 2880, 3840, 5760, 11520.
What is 11520 in binary?
10110100000000 (hexadecimal 2D00, octal 26400).
What is the square root of 11520?
About 107.3313, exactly 48√5.
Is 11520 divisible by 3?
Yes. Its digits add up to 9, a multiple of 3.
What is special about the number 11520?
11520 is a happy number: repeatedly adding the squares of its digits reaches 1; a Harshad number: divisible by its digit sum 9.