The number 3993
3993 is a palindrome: it reads 3993 backwards too. Its prime factorisation is 3 × . Divisors (8): 1, 3, 11, 33, 121, 363, 1331, 3993.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 3993: a palindrome: it reads 3993 backwards too.
- 2
3993 is composite. Its prime factorisation is
- 3
The divisors add up to 5856; without 3993 itself that is 1863, so 3993 is deficient (1863 is less than 3993). Euler's totient φ(3993) = 2420 numbers up to 3993 share no factor with it.
- 4
The digits of 3993 add up to 24, and repeating that until one digit is left gives the digital root 6. The Collatz sequence (halve if even, else 3n+1) takes 51 steps to reach 1.
LaTeX source of the formulas on this page
\[ 3993 = 3 \times 11^{3} \]3993 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 8 |
| Sum of divisors | 5856 |
| Euler totient φ(n) | 2420 |
| Square | 15944049 |
| Cube | 63664587657 |
| Square root | 63.190189 (= 11√33) |
| Digit sum / digital root | 24 / 6 |
| Collatz steps to 1 | 51 |
| Scientific notation | 3.993 × |
3993 in other forms
| Form | Value |
|---|---|
| In words | three thousand nine hundred and ninety-three |
| Roman numerals | MMMCMXCIII |
| Binary (base 2) | 111110011001 |
| Octal (base 8) | 7631 |
| Hexadecimal (base 16) | F99 |
| Base 3 | 12110220 |
| As time | 3993 seconds = 1 h 6 min 33 s |
Is 3993 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 (3993 ÷ 3 = 1331) | 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 3) | 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 3) | 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 1) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 6) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | No (remainder 3) | A number is divisible by 10 if the last digit is 0. |
| 11 | Yes (3993 ÷ 11 = 363) | 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 3993 a prime number?
No. 3993 = 3 × , so it is divisible by 3.
What are the factors of 3993?
1, 3, 11, 33, 121, 363, 1331, 3993.
What is 3993 in binary?
111110011001 (hexadecimal F99, octal 7631).
What is the square root of 3993?
About 63.1902, exactly 11√33.
What is 3993 in Roman numerals?
MMMCMXCIII.
Is 3993 divisible by 3?
Yes. Its digits add up to 24, a multiple of 3.
What is special about the number 3993?
3993 is a palindrome: it reads 3993 backwards too.