The number 12033
12033 is a composite number with 12 divisors. Its prime factorisation is × 7 × 191. Divisors (12): 1, 3, 7, 9, 21, 63, 191, 573, 1337, 1719, 4011, 12033.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 12033: a happy number: repeatedly adding the squares of its digits reaches 1; a Harshad number: divisible by its digit sum 9.
- 2
12033 is composite. Its prime factorisation is
- 3
The divisors add up to 19968; without 12033 itself that is 7935, so 12033 is deficient (7935 is less than 12033). Euler's totient φ(12033) = 6840 numbers up to 12033 share no factor with it.
- 4
The digits of 12033 add up to 9, and repeating that until one digit is left gives the digital root 9. The Collatz sequence (halve if even, else 3n+1) takes 50 steps to reach 1.
LaTeX source of the formulas on this page
\[ 12033 = 3^{2} \times 7 \times 191 \]12033 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 12 |
| Sum of divisors | 19968 |
| Euler totient φ(n) | 6840 |
| Square | 144793089 |
| Cube | 1742295239937 |
| Square root | 109.695032 (= 3√1337) |
| Digit sum / digital root | 9 / 9 |
| Collatz steps to 1 | 50 |
| Scientific notation | 1.2033 × |
12033 in other forms
| Form | Value |
|---|---|
| In words | twelve thousand and thirty-three |
| Binary (base 2) | 10111100000001 |
| Octal (base 8) | 27401 |
| Hexadecimal (base 16) | 2F01 |
| Base 3 | 121111200 |
| As time | 12033 seconds = 3 h 20 min 33 s |
Is 12033 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 (12033 ÷ 3 = 4011) | 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 | Yes (12033 ÷ 7 = 1719) | 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 (12033 ÷ 9 = 1337) | 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 9) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 12033 a prime number?
No. 12033 = × 7 × 191, so it is divisible by 3.
What are the factors of 12033?
1, 3, 7, 9, 21, 63, 191, 573, 1337, 1719, 4011, 12033.
What is 12033 in binary?
10111100000001 (hexadecimal 2F01, octal 27401).
What is the square root of 12033?
About 109.6950, exactly 3√1337.
Is 12033 divisible by 3?
Yes. Its digits add up to 9, a multiple of 3.
What is special about the number 12033?
12033 is a happy number: repeatedly adding the squares of its digits reaches 1; a Harshad number: divisible by its digit sum 9.