The number 11664
11664 is a perfect square (108²). Its prime factorisation is × . Divisors (35): 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 27, 36, 48, 54, 72 … 11664.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 11664: a perfect square (108²); a Harshad number: divisible by its digit sum 18.
- 2
11664 is composite. Its prime factorisation is
- 3
The divisors add up to 33883; without 11664 itself that is 22219, so 11664 is abundant (22219 is more than 11664). Euler's totient φ(11664) = 3888 numbers up to 11664 share no factor with it.
- 4
The digits of 11664 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 37 steps to reach 1.
LaTeX source of the formulas on this page
\[ 11664 = 2^{4} \times 3^{6} \]11664 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 35 |
| Sum of divisors | 33883 |
| Euler totient φ(n) | 3888 |
| Square | 136048896 |
| Cube | 1586874322944 |
| Square root | 108 |
| Digit sum / digital root | 18 / 9 |
| Collatz steps to 1 | 37 |
| Scientific notation | 1.1664 × |
| Perfect power |
11664 in other forms
| Form | Value |
|---|---|
| In words | eleven thousand six hundred and sixty-four |
| Binary (base 2) | 10110110010000 |
| Octal (base 8) | 26620 |
| Hexadecimal (base 16) | 2D90 |
| Base 3 | 121000000 |
| As time | 11664 seconds = 3 h 14 min 24 s |
Is 11664 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (11664 ÷ 2 = 5832) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (11664 ÷ 3 = 3888) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (11664 ÷ 4 = 2916) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | No (remainder 4) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (11664 ÷ 6 = 1944) | 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 (11664 ÷ 8 = 1458) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | Yes (11664 ÷ 9 = 1296) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | No (remainder 4) | 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 (11664 ÷ 12 = 972) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 11664 a prime number?
No. 11664 = × , so it is divisible by 2.
What are the factors of 11664?
1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 27, 36, 48, 54, 72, 81, 108, 144, 162, 216, 243, 324, 432, 486, 648, 729, 972, 1296, 1458, 1944, 2916, 3888, 5832, 11664.
What is 11664 in binary?
10110110010000 (hexadecimal 2D90, octal 26620).
What is the square root of 11664?
108, because 108 × 108 = 11664.
Is 11664 divisible by 3?
Yes. Its digits add up to 18, a multiple of 3.
What is special about the number 11664?
11664 is a perfect square (108²); a Harshad number: divisible by its digit sum 18.