The number 21664
21664 is a composite number with 12 divisors. Its prime factorisation is × 677. Divisors (12): 1, 2, 4, 8, 16, 32, 677, 1354, 2708, 5416, 10832, 21664.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
21664 has no famous special property in the usual lists (prime, square, cube, triangular, Fibonacci, palindrome, perfect), but it is still a composite number.
- 2
21664 is composite. Its prime factorisation is
- 3
The divisors add up to 42714; without 21664 itself that is 21050, so 21664 is deficient (21050 is less than 21664). Euler's totient φ(21664) = 10816 numbers up to 21664 share no factor with it.
- 4
The digits of 21664 add up to 19, and repeating that until one digit is left gives the digital root 1. The Collatz sequence (halve if even, else 3n+1) takes 56 steps to reach 1.
LaTeX source of the formulas on this page
\[ 21664 = 2^{5} \times 677 \]21664 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 12 |
| Sum of divisors | 42714 |
| Euler totient φ(n) | 10816 |
| Square | 469328896 |
| Cube | 10167541202944 |
| Square root | 147.186956 (= 4√1354) |
| Digit sum / digital root | 19 / 1 |
| Collatz steps to 1 | 56 |
| Scientific notation | 2.1664 × |
21664 in other forms
| Form | Value |
|---|---|
| In words | twenty-one thousand six hundred and sixty-four |
| Binary (base 2) | 101010010100000 |
| Octal (base 8) | 52240 |
| Hexadecimal (base 16) | 54A0 |
| Base 3 | 1002201101 |
| As time | 21664 seconds = 6 h 1 min 4 s |
Is 21664 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (21664 ÷ 2 = 10832) | 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 (21664 ÷ 4 = 5416) | 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 6) | 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 (21664 ÷ 8 = 2708) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 1) | 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 5) | 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 21664 a prime number?
No. 21664 = × 677, so it is divisible by 2.
What are the factors of 21664?
1, 2, 4, 8, 16, 32, 677, 1354, 2708, 5416, 10832, 21664.
What is 21664 in binary?
101010010100000 (hexadecimal 54A0, octal 52240).
What is the square root of 21664?
About 147.1870, exactly 4√1354.
Is 21664 divisible by 3?
No. Its digits add up to 19, which is not a multiple of 3.
What is special about the number 21664?
It is a composite number with 12 divisors.