The number 32993
32993 is the 3537th prime number. Its only divisors are 1 and 32993.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 32993: the 3537th prime number.
- 2
32993 is prime, so its only factors are 1 and 32993. It is the 3537th prime; the next prime is 32999 and the one before is 32987.
- 3
The divisors add up to 32994; without 32993 itself that is 1, so 32993 is deficient (1 is less than 32993). Euler's totient φ(32993) = 32992 numbers up to 32993 share no factor with it.
- 4
The digits of 32993 add up to 26, and repeating that until one digit is left gives the digital root 8. The Collatz sequence (halve if even, else 3n+1) takes 147 steps to reach 1.
32993 at a glance
| Property | Value |
|---|---|
| Type | prime |
| Number of divisors | 2 |
| Sum of divisors | 32994 |
| Euler totient φ(n) | 32992 |
| Square | 1088538049 |
| Cube | 35914135850657 |
| Square root | 181.639753 |
| Digit sum / digital root | 26 / 8 |
| Collatz steps to 1 | 147 |
| Scientific notation | 3.2993 × |
32993 in other forms
| Form | Value |
|---|---|
| In words | thirty-two thousand nine hundred and ninety-three |
| Binary (base 2) | 1000000011100001 |
| Octal (base 8) | 100341 |
| Hexadecimal (base 16) | 80E1 |
| Base 3 | 1200020222 |
| As time | 32993 seconds = 9 h 9 min 53 s |
Is 32993 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 | No (remainder 2) | 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 5) | 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 1) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 8) | 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 4) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | No (remainder 5) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 32993 a prime number?
Yes. 32993 is divisible only by 1 and itself.
What are the factors of 32993?
1, 32993.
What is 32993 in binary?
1000000011100001 (hexadecimal 80E1, octal 100341).
What is the square root of 32993?
About 181.6398.
Is 32993 divisible by 3?
No. Its digits add up to 26, which is not a multiple of 3.
What is special about the number 32993?
32993 is the 3537th prime number.