The number 33993
33993 is a composite number with 8 divisors. Its prime factorisation is × 1259. Divisors (8): 1, 3, 9, 27, 1259, 3777, 11331, 33993.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 33993: a Harshad number: divisible by its digit sum 27.
- 2
33993 is composite. Its prime factorisation is
- 3
The divisors add up to 50400; without 33993 itself that is 16407, so 33993 is deficient (16407 is less than 33993). Euler's totient φ(33993) = 22644 numbers up to 33993 share no factor with it.
- 4
The digits of 33993 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 85 steps to reach 1.
LaTeX source of the formulas on this page
\[ 33993 = 3^{3} \times 1259 \]33993 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 8 |
| Sum of divisors | 50400 |
| Euler totient φ(n) | 22644 |
| Square | 1155524049 |
| Cube | 39279728997657 |
| Square root | 184.371907 (= 3√3777) |
| Digit sum / digital root | 27 / 9 |
| Collatz steps to 1 | 85 |
| Scientific notation | 3.3993 × |
33993 in other forms
| Form | Value |
|---|---|
| In words | thirty-three thousand nine hundred and ninety-three |
| Binary (base 2) | 1000010011001001 |
| Octal (base 8) | 102311 |
| Hexadecimal (base 16) | 84C9 |
| Base 3 | 1201122000 |
| As time | 33993 seconds = 9 h 26 min 33 s |
Is 33993 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 (33993 ÷ 3 = 11331) | 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 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 | No (remainder 1) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | Yes (33993 ÷ 9 = 3777) | 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 | No (remainder 3) | 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 33993 a prime number?
No. 33993 = × 1259, so it is divisible by 3.
What are the factors of 33993?
1, 3, 9, 27, 1259, 3777, 11331, 33993.
What is 33993 in binary?
1000010011001001 (hexadecimal 84C9, octal 102311).
What is the square root of 33993?
About 184.3719, exactly 3√3777.
Is 33993 divisible by 3?
Yes. Its digits add up to 27, a multiple of 3.
What is special about the number 33993?
33993 is a Harshad number: divisible by its digit sum 27.