The number 13624
13624 is a composite number with 16 divisors. Its prime factorisation is × 13 × 131. Divisors (16): 1, 2, 4, 8, 13, 26, 52, 104, 131, 262, 524, 1048, 1703, 3406, 6812, 13624.
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How to work it out
- 1
13624 has no famous special property in the usual lists (prime, square, cube, triangular, Fibonacci, palindrome, perfect), but it is still a composite number.
- 2
13624 is composite. Its prime factorisation is
- 3
The divisors add up to 27720; without 13624 itself that is 14096, so 13624 is abundant (14096 is more than 13624). Euler's totient φ(13624) = 6240 numbers up to 13624 share no factor with it.
- 4
The digits of 13624 add up to 16, and repeating that until one digit is left gives the digital root 7. The Collatz sequence (halve if even, else 3n+1) takes 63 steps to reach 1.
LaTeX source of the formulas on this page
\[ 13624 = 2^{3} \times 13 \times 131 \]13624 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 16 |
| Sum of divisors | 27720 |
| Euler totient φ(n) | 6240 |
| Square | 185613376 |
| Cube | 2528796634624 |
| Square root | 116.721892 (= 2√3406) |
| Digit sum / digital root | 16 / 7 |
| Collatz steps to 1 | 63 |
| Scientific notation | 1.3624 × |
13624 in other forms
| Form | Value |
|---|---|
| In words | thirteen thousand six hundred and twenty-four |
| Binary (base 2) | 11010100111000 |
| Octal (base 8) | 32470 |
| Hexadecimal (base 16) | 3538 |
| Base 3 | 200200121 |
| As time | 13624 seconds = 3 h 47 min 4 s |
Is 13624 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (13624 ÷ 2 = 6812) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | No (remainder 1) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (13624 ÷ 4 = 3406) | 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 | No (remainder 4) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 2) | 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 (13624 ÷ 8 = 1703) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 7) | 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 6) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | No (remainder 4) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 13624 a prime number?
No. 13624 = × 13 × 131, so it is divisible by 2.
What are the factors of 13624?
1, 2, 4, 8, 13, 26, 52, 104, 131, 262, 524, 1048, 1703, 3406, 6812, 13624.
What is 13624 in binary?
11010100111000 (hexadecimal 3538, octal 32470).
What is the square root of 13624?
About 116.7219, exactly 2√3406.
Is 13624 divisible by 3?
No. Its digits add up to 16, which is not a multiple of 3.
What is special about the number 13624?
It is a composite number with 16 divisors.