The number 13221
13221 is a composite number with 12 divisors. Its prime factorisation is × 13 × 113. Divisors (12): 1, 3, 9, 13, 39, 113, 117, 339, 1017, 1469, 4407, 13221.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 13221: a happy number: repeatedly adding the squares of its digits reaches 1; a Harshad number: divisible by its digit sum 9.
- 2
13221 is composite. Its prime factorisation is
- 3
The divisors add up to 20748; without 13221 itself that is 7527, so 13221 is deficient (7527 is less than 13221). Euler's totient φ(13221) = 8064 numbers up to 13221 share no factor with it.
- 4
The digits of 13221 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
\[ 13221 = 3^{2} \times 13 \times 113 \]13221 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 12 |
| Sum of divisors | 20748 |
| Euler totient φ(n) | 8064 |
| Square | 174794841 |
| Cube | 2310962592861 |
| Square root | 114.982607 (= 3√1469) |
| Digit sum / digital root | 9 / 9 |
| Collatz steps to 1 | 50 |
| Scientific notation | 1.3221 × |
13221 in other forms
| Form | Value |
|---|---|
| In words | thirteen thousand two hundred and twenty-one |
| Binary (base 2) | 11001110100101 |
| Octal (base 8) | 31645 |
| Hexadecimal (base 16) | 33A5 |
| Base 3 | 200010200 |
| As time | 13221 seconds = 3 h 40 min 21 s |
Is 13221 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 (13221 ÷ 3 = 4407) | 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 5) | 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 (13221 ÷ 9 = 1469) | 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 13221 a prime number?
No. 13221 = × 13 × 113, so it is divisible by 3.
What are the factors of 13221?
1, 3, 9, 13, 39, 113, 117, 339, 1017, 1469, 4407, 13221.
What is 13221 in binary?
11001110100101 (hexadecimal 33A5, octal 31645).
What is the square root of 13221?
About 114.9826, exactly 3√1469.
Is 13221 divisible by 3?
Yes. Its digits add up to 9, a multiple of 3.
What is special about the number 13221?
13221 is a happy number: repeatedly adding the squares of its digits reaches 1; a Harshad number: divisible by its digit sum 9.