The number 1033
1033 is a twin prime (1031 and 1033 are both prime) and the 174th prime number. Its only divisors are 1 and 1033.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 1033: a twin prime (1031 and 1033 are both prime); the 174th prime number; a happy number: repeatedly adding the squares of its digits reaches 1.
- 2
1033 is prime, so its only factors are 1 and 1033. It is the 174th prime; the next prime is 1039 and the one before is 1031.
- 3
The divisors add up to 1034; without 1033 itself that is 1, so 1033 is deficient (1 is less than 1033). Euler's totient φ(1033) = 1032 numbers up to 1033 share no factor with it.
- 4
The digits of 1033 add up to 7, and repeating that until one digit is left gives the digital root 7. The Collatz sequence (halve if even, else 3n+1) takes 155 steps to reach 1.
1033 at a glance
| Property | Value |
|---|---|
| Type | prime |
| Number of divisors | 2 |
| Sum of divisors | 1034 |
| Euler totient φ(n) | 1032 |
| Square | 1067089 |
| Cube | 1102302937 |
| Square root | 32.140317 |
| Digit sum / digital root | 7 / 7 |
| Collatz steps to 1 | 155 |
| Scientific notation | 1.033 × |
1033 in other forms
| Form | Value |
|---|---|
| In words | one thousand and thirty-three |
| Roman numerals | MXXXIII |
| Binary (base 2) | 10000001001 |
| Octal (base 8) | 2011 |
| Hexadecimal (base 16) | 409 |
| Base 3 | 1102021 |
| As time | 1033 seconds = 17 min 13 s |
Is 1033 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 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 1) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 7) | 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 10) | 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 1033 a prime number?
Yes. 1033 is divisible only by 1 and itself.
What are the factors of 1033?
1, 1033.
What is 1033 in binary?
10000001001 (hexadecimal 409, octal 2011).
What is the square root of 1033?
About 32.1403.
What is 1033 in Roman numerals?
MXXXIII.
Is 1033 divisible by 3?
No. Its digits add up to 7, which is not a multiple of 3.
What is special about the number 1033?
1033 is a twin prime (1031 and 1033 are both prime); the 174th prime number; a happy number: repeatedly adding the squares of its digits reaches 1.