The number 13664
13664 is a composite number with 24 divisors. Its prime factorisation is × 7 × 61. Divisors (24): 1, 2, 4, 7, 8, 14, 16, 28, 32, 56, 61, 112, 122, 224, 244, 427 … 13664.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
13664 has no famous special property in the usual lists (prime, square, cube, triangular, Fibonacci, palindrome, perfect), but it is still a composite number.
- 2
13664 is composite. Its prime factorisation is
- 3
The divisors add up to 31248; without 13664 itself that is 17584, so 13664 is abundant (17584 is more than 13664). Euler's totient φ(13664) = 5760 numbers up to 13664 share no factor with it.
- 4
The digits of 13664 add up to 20, and repeating that until one digit is left gives the digital root 2. The Collatz sequence (halve if even, else 3n+1) takes 58 steps to reach 1.
LaTeX source of the formulas on this page
\[ 13664 = 2^{5} \times 7 \times 61 \]13664 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 24 |
| Sum of divisors | 31248 |
| Euler totient φ(n) | 5760 |
| Square | 186704896 |
| Cube | 2551135698944 |
| Square root | 116.893114 (= 4√854) |
| Digit sum / digital root | 20 / 2 |
| Collatz steps to 1 | 58 |
| Scientific notation | 1.3664 × |
13664 in other forms
| Form | Value |
|---|---|
| In words | thirteen thousand six hundred and sixty-four |
| Binary (base 2) | 11010101100000 |
| Octal (base 8) | 32540 |
| Hexadecimal (base 16) | 3560 |
| Base 3 | 200202002 |
| As time | 13664 seconds = 3 h 47 min 44 s |
Is 13664 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (13664 ÷ 2 = 6832) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | No (remainder 2) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (13664 ÷ 4 = 3416) | 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 2) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | Yes (13664 ÷ 7 = 1952) | 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 (13664 ÷ 8 = 1708) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 2) | 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 | No (remainder 8) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 13664 a prime number?
No. 13664 = × 7 × 61, so it is divisible by 2.
What are the factors of 13664?
1, 2, 4, 7, 8, 14, 16, 28, 32, 56, 61, 112, 122, 224, 244, 427, 488, 854, 976, 1708, 1952, 3416, 6832, 13664.
What is 13664 in binary?
11010101100000 (hexadecimal 3560, octal 32540).
What is the square root of 13664?
About 116.8931, exactly 4√854.
Is 13664 divisible by 3?
No. Its digits add up to 20, which is not a multiple of 3.
What is special about the number 13664?
It is a composite number with 24 divisors.