The number 11712
11712 is a composite number with 28 divisors. Its prime factorisation is × 3 × 61. Divisors (28): 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 61, 64, 96, 122, 183 … 11712.
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How to work it out
- 1
What is special about 11712: a Harshad number: divisible by its digit sum 12.
- 2
11712 is composite. Its prime factorisation is
- 3
The divisors add up to 31496; without 11712 itself that is 19784, so 11712 is abundant (19784 is more than 11712). Euler's totient φ(11712) = 3840 numbers up to 11712 share no factor with it.
- 4
The digits of 11712 add up to 12, and repeating that until one digit is left gives the digital root 3. The Collatz sequence (halve if even, else 3n+1) takes 99 steps to reach 1.
LaTeX source of the formulas on this page
\[ 11712 = 2^{6} \times 3 \times 61 \]11712 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 28 |
| Sum of divisors | 31496 |
| Euler totient φ(n) | 3840 |
| Square | 137170944 |
| Cube | 1606546096128 |
| Square root | 108.221994 (= 8√183) |
| Digit sum / digital root | 12 / 3 |
| Collatz steps to 1 | 99 |
| Scientific notation | 1.1712 × |
11712 in other forms
| Form | Value |
|---|---|
| In words | eleven thousand seven hundred and twelve |
| Binary (base 2) | 10110111000000 |
| Octal (base 8) | 26700 |
| Hexadecimal (base 16) | 2DC0 |
| Base 3 | 121001210 |
| As time | 11712 seconds = 3 h 15 min 12 s |
Is 11712 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (11712 ÷ 2 = 5856) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (11712 ÷ 3 = 3904) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (11712 ÷ 4 = 2928) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | No (remainder 2) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (11712 ÷ 6 = 1952) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 1) | 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 (11712 ÷ 8 = 1464) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 3) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | No (remainder 2) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 8) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (11712 ÷ 12 = 976) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 11712 a prime number?
No. 11712 = × 3 × 61, so it is divisible by 2.
What are the factors of 11712?
1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 61, 64, 96, 122, 183, 192, 244, 366, 488, 732, 976, 1464, 1952, 2928, 3904, 5856, 11712.
What is 11712 in binary?
10110111000000 (hexadecimal 2DC0, octal 26700).
What is the square root of 11712?
About 108.2220, exactly 8√183.
Is 11712 divisible by 3?
Yes. Its digits add up to 12, a multiple of 3.
What is special about the number 11712?
11712 is a Harshad number: divisible by its digit sum 12.