The number 33023
33023 is the 3540th prime number. Its only divisors are 1 and 33023.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 33023: the 3540th prime number; a happy number: repeatedly adding the squares of its digits reaches 1.
- 2
33023 is prime, so its only factors are 1 and 33023. It is the 3540th prime; the next prime is 33029 and the one before is 33013.
- 3
The divisors add up to 33024; without 33023 itself that is 1, so 33023 is deficient (1 is less than 33023). Euler's totient φ(33023) = 33022 numbers up to 33023 share no factor with it.
- 4
The digits of 33023 add up to 11, and repeating that until one digit is left gives the digital root 2. The Collatz sequence (halve if even, else 3n+1) takes 72 steps to reach 1.
33023 at a glance
| Property | Value |
|---|---|
| Type | prime |
| Number of divisors | 2 |
| Sum of divisors | 33024 |
| Euler totient φ(n) | 33022 |
| Square | 1090518529 |
| Cube | 36012193383167 |
| Square root | 181.722316 |
| Digit sum / digital root | 11 / 2 |
| Collatz steps to 1 | 72 |
| Scientific notation | 3.3023 × |
33023 in other forms
| Form | Value |
|---|---|
| In words | thirty-three thousand and twenty-three |
| Binary (base 2) | 1000000011111111 |
| Octal (base 8) | 100377 |
| Hexadecimal (base 16) | 80FF |
| Base 3 | 1200022002 |
| As time | 33023 seconds = 9 h 10 min 23 s |
Is 33023 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 3) | 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 4) | 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 2) | 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 1) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | No (remainder 11) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 33023 a prime number?
Yes. 33023 is divisible only by 1 and itself.
What are the factors of 33023?
1, 33023.
What is 33023 in binary?
1000000011111111 (hexadecimal 80FF, octal 100377).
What is the square root of 33023?
About 181.7223.
Is 33023 divisible by 3?
No. Its digits add up to 11, which is not a multiple of 3.
What is special about the number 33023?
33023 is the 3540th prime number; a happy number: repeatedly adding the squares of its digits reaches 1.