The number 13033
13033 is the 1552nd prime number. Its only divisors are 1 and 13033.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 13033: the 1552nd prime number; a happy number: repeatedly adding the squares of its digits reaches 1.
- 2
13033 is prime, so its only factors are 1 and 13033. It is the 1552nd prime; the next prime is 13037 and the one before is 13009.
- 3
The divisors add up to 13034; without 13033 itself that is 1, so 13033 is deficient (1 is less than 13033). Euler's totient φ(13033) = 13032 numbers up to 13033 share no factor with it.
- 4
The digits of 13033 add up to 10, and repeating that until one digit is left gives the digital root 1. The Collatz sequence (halve if even, else 3n+1) takes 156 steps to reach 1.
13033 at a glance
| Property | Value |
|---|---|
| Type | prime |
| Number of divisors | 2 |
| Sum of divisors | 13034 |
| Euler totient φ(n) | 13032 |
| Square | 169859089 |
| Cube | 2213773506937 |
| Square root | 114.162165 |
| Digit sum / digital root | 10 / 1 |
| Collatz steps to 1 | 156 |
| Scientific notation | 1.3033 × |
13033 in other forms
| Form | Value |
|---|---|
| In words | thirteen thousand and thirty-three |
| Binary (base 2) | 11001011101001 |
| Octal (base 8) | 31351 |
| Hexadecimal (base 16) | 32E9 |
| Base 3 | 122212201 |
| As time | 13033 seconds = 3 h 37 min 13 s |
Is 13033 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 1) | 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 1) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 6) | 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 1) | 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 9) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | No (remainder 1) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 13033 a prime number?
Yes. 13033 is divisible only by 1 and itself.
What are the factors of 13033?
1, 13033.
What is 13033 in binary?
11001011101001 (hexadecimal 32E9, octal 31351).
What is the square root of 13033?
About 114.1622.
Is 13033 divisible by 3?
No. Its digits add up to 10, which is not a multiple of 3.
What is special about the number 13033?
13033 is the 1552nd prime number; a happy number: repeatedly adding the squares of its digits reaches 1.