The number 13212
13212 is a composite number with 18 divisors. Its prime factorisation is × × 367. Divisors (18): 1, 2, 3, 4, 6, 9, 12, 18, 36, 367, 734, 1101, 1468, 2202, 3303, 4404 … 13212.
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How to work it out
- 1
What is special about 13212: a happy number: repeatedly adding the squares of its digits reaches 1; a Harshad number: divisible by its digit sum 9.
- 2
13212 is composite. Its prime factorisation is
- 3
The divisors add up to 33488; without 13212 itself that is 20276, so 13212 is abundant (20276 is more than 13212). Euler's totient φ(13212) = 4392 numbers up to 13212 share no factor with it.
- 4
The digits of 13212 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 76 steps to reach 1.
LaTeX source of the formulas on this page
\[ 13212 = 2^{2} \times 3^{2} \times 367 \]13212 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 18 |
| Sum of divisors | 33488 |
| Euler totient φ(n) | 4392 |
| Square | 174556944 |
| Cube | 2306246344128 |
| Square root | 114.943464 (= 6√367) |
| Digit sum / digital root | 9 / 9 |
| Collatz steps to 1 | 76 |
| Scientific notation | 1.3212 × |
13212 in other forms
| Form | Value |
|---|---|
| In words | thirteen thousand two hundred and twelve |
| Binary (base 2) | 11001110011100 |
| Octal (base 8) | 31634 |
| Hexadecimal (base 16) | 339C |
| Base 3 | 200010100 |
| As time | 13212 seconds = 3 h 40 min 12 s |
Is 13212 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (13212 ÷ 2 = 6606) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (13212 ÷ 3 = 4404) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (13212 ÷ 4 = 3303) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | No (remainder 2) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (13212 ÷ 6 = 2202) | 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 4) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | Yes (13212 ÷ 9 = 1468) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | No (remainder 2) | 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 | Yes (13212 ÷ 12 = 1101) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 13212 a prime number?
No. 13212 = × × 367, so it is divisible by 2.
What are the factors of 13212?
1, 2, 3, 4, 6, 9, 12, 18, 36, 367, 734, 1101, 1468, 2202, 3303, 4404, 6606, 13212.
What is 13212 in binary?
11001110011100 (hexadecimal 339C, octal 31634).
What is the square root of 13212?
About 114.9435, exactly 6√367.
Is 13212 divisible by 3?
Yes. Its digits add up to 9, a multiple of 3.
What is special about the number 13212?
13212 is a happy number: repeatedly adding the squares of its digits reaches 1; a Harshad number: divisible by its digit sum 9.