The number 3213
3213 is a composite number with 16 divisors. Its prime factorisation is × 7 × 17. Divisors (16): 1, 3, 7, 9, 17, 21, 27, 51, 63, 119, 153, 189, 357, 459, 1071, 3213.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 3213: a happy number: repeatedly adding the squares of its digits reaches 1; a Harshad number: divisible by its digit sum 9.
- 2
3213 is composite. Its prime factorisation is
- 3
The divisors add up to 5760; without 3213 itself that is 2547, so 3213 is deficient (2547 is less than 3213). Euler's totient φ(3213) = 1728 numbers up to 3213 share no factor with it.
- 4
The digits of 3213 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 22 steps to reach 1.
LaTeX source of the formulas on this page
\[ 3213 = 3^{3} \times 7 \times 17 \]3213 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 16 |
| Sum of divisors | 5760 |
| Euler totient φ(n) | 1728 |
| Square | 10323369 |
| Cube | 33168984597 |
| Square root | 56.683331 (= 3√357) |
| Digit sum / digital root | 9 / 9 |
| Collatz steps to 1 | 22 |
| Scientific notation | 3.213 × |
3213 in other forms
| Form | Value |
|---|---|
| In words | three thousand two hundred and thirteen |
| Roman numerals | MMMCCXIII |
| Binary (base 2) | 110010001101 |
| Octal (base 8) | 6215 |
| Hexadecimal (base 16) | C8D |
| Base 3 | 11102000 |
| As time | 3213 seconds = 53 min 33 s |
Is 3213 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 (3213 ÷ 3 = 1071) | 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 (3213 ÷ 7 = 459) | 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 5) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | Yes (3213 ÷ 9 = 357) | 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 9) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 3213 a prime number?
No. 3213 = × 7 × 17, so it is divisible by 3.
What are the factors of 3213?
1, 3, 7, 9, 17, 21, 27, 51, 63, 119, 153, 189, 357, 459, 1071, 3213.
What is 3213 in binary?
110010001101 (hexadecimal C8D, octal 6215).
What is the square root of 3213?
About 56.6833, exactly 3√357.
What is 3213 in Roman numerals?
MMMCCXIII.
Is 3213 divisible by 3?
Yes. Its digits add up to 9, a multiple of 3.
What is special about the number 3213?
3213 is a happy number: repeatedly adding the squares of its digits reaches 1; a Harshad number: divisible by its digit sum 9.