The number 13224
13224 is a composite number with 32 divisors. Its prime factorisation is × 3 × 19 × 29. Divisors (32): 1, 2, 3, 4, 6, 8, 12, 19, 24, 29, 38, 57, 58, 76, 87, 114 … 13224.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 13224: a Harshad number: divisible by its digit sum 12.
- 2
13224 is composite. Its prime factorisation is
- 3
The divisors add up to 36000; without 13224 itself that is 22776, so 13224 is abundant (22776 is more than 13224). Euler's totient φ(13224) = 4032 numbers up to 13224 share no factor with it.
- 4
The digits of 13224 add up to 12, and repeating that until one digit is left gives the digital root 3. The Collatz sequence (halve if even, else 3n+1) takes 94 steps to reach 1.
LaTeX source of the formulas on this page
\[ 13224 = 2^{3} \times 3 \times 19 \times 29 \]13224 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 32 |
| Sum of divisors | 36000 |
| Euler totient φ(n) | 4032 |
| Square | 174874176 |
| Cube | 2312536103424 |
| Square root | 114.995652 (= 2√3306) |
| Digit sum / digital root | 12 / 3 |
| Collatz steps to 1 | 94 |
| Scientific notation | 1.3224 × |
13224 in other forms
| Form | Value |
|---|---|
| In words | thirteen thousand two hundred and twenty-four |
| Binary (base 2) | 11001110101000 |
| Octal (base 8) | 31650 |
| Hexadecimal (base 16) | 33A8 |
| Base 3 | 200010210 |
| As time | 13224 seconds = 3 h 40 min 24 s |
Is 13224 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (13224 ÷ 2 = 6612) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (13224 ÷ 3 = 4408) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (13224 ÷ 4 = 3306) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | No (remainder 4) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (13224 ÷ 6 = 2204) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 1) | 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 | Yes (13224 ÷ 8 = 1653) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 3) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | No (remainder 4) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 2) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (13224 ÷ 12 = 1102) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 13224 a prime number?
No. 13224 = × 3 × 19 × 29, so it is divisible by 2.
What are the factors of 13224?
1, 2, 3, 4, 6, 8, 12, 19, 24, 29, 38, 57, 58, 76, 87, 114, 116, 152, 174, 228, 232, 348, 456, 551, 696, 1102, 1653, 2204, 3306, 4408, 6612, 13224.
What is 13224 in binary?
11001110101000 (hexadecimal 33A8, octal 31650).
What is the square root of 13224?
About 114.9957, exactly 2√3306.
Is 13224 divisible by 3?
Yes. Its digits add up to 12, a multiple of 3.
What is special about the number 13224?
13224 is a Harshad number: divisible by its digit sum 12.