The number 3321
3321 is a triangular number: 1 + 2 + … + 81 = 3321. Its prime factorisation is × 41. Divisors (10): 1, 3, 9, 27, 41, 81, 123, 369, 1107, 3321.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 3321: a triangular number: 1 + 2 + … + 81 = 3321; a happy number: repeatedly adding the squares of its digits reaches 1; a Harshad number: divisible by its digit sum 9.
- 2
3321 is composite. Its prime factorisation is
- 3
The divisors add up to 5082; without 3321 itself that is 1761, so 3321 is deficient (1761 is less than 3321). Euler's totient φ(3321) = 2160 numbers up to 3321 share no factor with it.
- 4
The digits of 3321 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 105 steps to reach 1.
LaTeX source of the formulas on this page
\[ 3321 = 3^{4} \times 41 \]3321 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 10 |
| Sum of divisors | 5082 |
| Euler totient φ(n) | 2160 |
| Square | 11029041 |
| Cube | 36627445161 |
| Square root | 57.628118 (= 9√41) |
| Digit sum / digital root | 9 / 9 |
| Collatz steps to 1 | 105 |
| Scientific notation | 3.321 × |
3321 in other forms
| Form | Value |
|---|---|
| In words | three thousand three hundred and twenty-one |
| Roman numerals | MMMCCCXXI |
| Binary (base 2) | 110011111001 |
| Octal (base 8) | 6371 |
| Hexadecimal (base 16) | CF9 |
| Base 3 | 11120000 |
| As time | 3321 seconds = 55 min 21 s |
Is 3321 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 (3321 ÷ 3 = 1107) | 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 1) | 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 | No (remainder 3) | 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 (3321 ÷ 9 = 369) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | No (remainder 1) | 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 3321 a prime number?
No. 3321 = × 41, so it is divisible by 3.
What are the factors of 3321?
1, 3, 9, 27, 41, 81, 123, 369, 1107, 3321.
What is 3321 in binary?
110011111001 (hexadecimal CF9, octal 6371).
What is the square root of 3321?
About 57.6281, exactly 9√41.
What is 3321 in Roman numerals?
MMMCCCXXI.
Is 3321 divisible by 3?
Yes. Its digits add up to 9, a multiple of 3.
What is special about the number 3321?
3321 is a triangular number: 1 + 2 + … + 81 = 3321; a happy number: repeatedly adding the squares of its digits reaches 1; a Harshad number: divisible by its digit sum 9.