The number 3999
3999 is a binary palindrome (111110011111). Its prime factorisation is 3 × 31 × 43. Divisors (8): 1, 3, 31, 43, 93, 129, 1333, 3999.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 3999: a binary palindrome (111110011111).
- 2
3999 is composite. Its prime factorisation is
- 3
The divisors add up to 5632; without 3999 itself that is 1633, so 3999 is deficient (1633 is less than 3999). Euler's totient φ(3999) = 2520 numbers up to 3999 share no factor with it.
- 4
The digits of 3999 add up to 30, and repeating that until one digit is left gives the digital root 3. The Collatz sequence (halve if even, else 3n+1) takes 188 steps to reach 1.
LaTeX source of the formulas on this page
\[ 3999 = 3 \times 31 \times 43 \]
3999 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 8 |
| Sum of divisors | 5632 |
| Euler totient φ(n) | 2520 |
| Square | 15992001 |
| Cube | 63952011999 |
| Square root | 63.237647 |
| Digit sum / digital root | 30 / 3 |
| Collatz steps to 1 | 188 |
| Scientific notation | 3.999 × |
3999 in other forms
| Form | Value |
|---|---|
| In words | three thousand nine hundred and ninety-nine |
| Roman numerals | MMMCMXCIX |
| Binary (base 2) | 111110011111 |
| Octal (base 8) | 7637 |
| Hexadecimal (base 16) | F9F |
| Base 3 | 12111010 |
| As time | 3999 seconds = 1 h 6 min 39 s |
Is 3999 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 (3999 ÷ 3 = 1333) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | No (remainder 3) | 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 | No (remainder 3) | 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 | No (remainder 7) | 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 9) | 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 | No (remainder 3) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 3999 a prime number?
No. 3999 = 3 × 31 × 43, so it is divisible by 3.
What are the factors of 3999?
1, 3, 31, 43, 93, 129, 1333, 3999.
What is 3999 in binary?
111110011111 (hexadecimal F9F, octal 7637).
What is the square root of 3999?
About 63.2376.
What is 3999 in Roman numerals?
MMMCMXCIX.
Is 3999 divisible by 3?
Yes. Its digits add up to 30, a multiple of 3.
What is special about the number 3999?
3999 is a binary palindrome (111110011111).