The number 13644
13644 is a composite number with 18 divisors. Its prime factorisation is × × 379. Divisors (18): 1, 2, 3, 4, 6, 9, 12, 18, 36, 379, 758, 1137, 1516, 2274, 3411, 4548 … 13644.
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How to work it out
- 1
What is special about 13644: a Harshad number: divisible by its digit sum 18.
- 2
13644 is composite. Its prime factorisation is
- 3
The divisors add up to 34580; without 13644 itself that is 20936, so 13644 is abundant (20936 is more than 13644). Euler's totient φ(13644) = 4536 numbers up to 13644 share no factor with it.
- 4
The digits of 13644 add up to 18, and repeating that until one digit is left gives the digital root 9. The Collatz sequence (halve if even, else 3n+1) takes 138 steps to reach 1.
LaTeX source of the formulas on this page
\[ 13644 = 2^{2} \times 3^{2} \times 379 \]13644 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 18 |
| Sum of divisors | 34580 |
| Euler totient φ(n) | 4536 |
| Square | 186158736 |
| Cube | 2539949793984 |
| Square root | 116.807534 (= 6√379) |
| Digit sum / digital root | 18 / 9 |
| Collatz steps to 1 | 138 |
| Scientific notation | 1.3644 × |
13644 in other forms
| Form | Value |
|---|---|
| In words | thirteen thousand six hundred and forty-four |
| Binary (base 2) | 11010101001100 |
| Octal (base 8) | 32514 |
| Hexadecimal (base 16) | 354C |
| Base 3 | 200201100 |
| As time | 13644 seconds = 3 h 47 min 24 s |
Is 13644 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (13644 ÷ 2 = 6822) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (13644 ÷ 3 = 4548) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (13644 ÷ 4 = 3411) | 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 (13644 ÷ 6 = 2274) | 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 | No (remainder 4) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | Yes (13644 ÷ 9 = 1516) | 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 4) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (13644 ÷ 12 = 1137) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 13644 a prime number?
No. 13644 = × × 379, so it is divisible by 2.
What are the factors of 13644?
1, 2, 3, 4, 6, 9, 12, 18, 36, 379, 758, 1137, 1516, 2274, 3411, 4548, 6822, 13644.
What is 13644 in binary?
11010101001100 (hexadecimal 354C, octal 32514).
What is the square root of 13644?
About 116.8075, exactly 6√379.
Is 13644 divisible by 3?
Yes. Its digits add up to 18, a multiple of 3.
What is special about the number 13644?
13644 is a Harshad number: divisible by its digit sum 18.