The number 11997
11997 is a binary palindrome (10111011011101). Its prime factorisation is × 31 × 43. Divisors (12): 1, 3, 9, 31, 43, 93, 129, 279, 387, 1333, 3999, 11997.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 11997: a binary palindrome (10111011011101).
- 2
11997 is composite. Its prime factorisation is
- 3
The divisors add up to 18304; without 11997 itself that is 6307, so 11997 is deficient (6307 is less than 11997). Euler's totient φ(11997) = 7560 numbers up to 11997 share no factor with it.
- 4
The digits of 11997 add up to 27, and repeating that until one digit is left gives the digital root 9. The Collatz sequence (halve if even, else 3n+1) takes 50 steps to reach 1.
LaTeX source of the formulas on this page
\[ 11997 = 3^{2} \times 31 \times 43 \]11997 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 12 |
| Sum of divisors | 18304 |
| Euler totient φ(n) | 7560 |
| Square | 143928009 |
| Cube | 1726704323973 |
| Square root | 109.530818 (= 3√1333) |
| Digit sum / digital root | 27 / 9 |
| Collatz steps to 1 | 50 |
| Scientific notation | 1.1997 × |
11997 in other forms
| Form | Value |
|---|---|
| In words | eleven thousand nine hundred and ninety-seven |
| Binary (base 2) | 10111011011101 |
| Octal (base 8) | 27335 |
| Hexadecimal (base 16) | 2EDD |
| Base 3 | 121110100 |
| As time | 11997 seconds = 3 h 19 min 57 s |
Is 11997 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | No (remainder 1) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (11997 ÷ 3 = 3999) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | No (remainder 1) | 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 | No (remainder 3) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 6) | 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 | No (remainder 5) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | Yes (11997 ÷ 9 = 1333) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | No (remainder 7) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 7) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | No (remainder 9) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 11997 a prime number?
No. 11997 = × 31 × 43, so it is divisible by 3.
What are the factors of 11997?
1, 3, 9, 31, 43, 93, 129, 279, 387, 1333, 3999, 11997.
What is 11997 in binary?
10111011011101 (hexadecimal 2EDD, octal 27335).
What is the square root of 11997?
About 109.5308, exactly 3√1333.
Is 11997 divisible by 3?
Yes. Its digits add up to 27, a multiple of 3.
What is special about the number 11997?
11997 is a binary palindrome (10111011011101).