The number 21312
21312 is a palindrome: it reads 21312 backwards too. Its prime factorisation is × × 37. Divisors (42): 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 32, 36, 37, 48, 64 … 21312.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 21312: a palindrome: it reads 21312 backwards too; a happy number: repeatedly adding the squares of its digits reaches 1; a Harshad number: divisible by its digit sum 9.
- 2
21312 is composite. Its prime factorisation is
- 3
The divisors add up to 62738; without 21312 itself that is 41426, so 21312 is abundant (41426 is more than 21312). Euler's totient φ(21312) = 6912 numbers up to 21312 share no factor with it.
- 4
The digits of 21312 add up to 9, and repeating that until one digit is left gives the digital root 9. The Collatz sequence (halve if even, else 3n+1) takes 118 steps to reach 1.
LaTeX source of the formulas on this page
\[ 21312 = 2^{6} \times 3^{2} \times 37 \]21312 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 42 |
| Sum of divisors | 62738 |
| Euler totient φ(n) | 6912 |
| Square | 454201344 |
| Cube | 9679939043328 |
| Square root | 145.986301 (= 24√37) |
| Digit sum / digital root | 9 / 9 |
| Collatz steps to 1 | 118 |
| Scientific notation | 2.1312 × |
21312 in other forms
| Form | Value |
|---|---|
| In words | twenty-one thousand three hundred and twelve |
| Binary (base 2) | 101001101000000 |
| Octal (base 8) | 51500 |
| Hexadecimal (base 16) | 5340 |
| Base 3 | 1002020100 |
| As time | 21312 seconds = 5 h 55 min 12 s |
Is 21312 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (21312 ÷ 2 = 10656) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (21312 ÷ 3 = 7104) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (21312 ÷ 4 = 5328) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | No (remainder 2) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (21312 ÷ 6 = 3552) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 4) | 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 (21312 ÷ 8 = 2664) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | Yes (21312 ÷ 9 = 2368) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | No (remainder 2) | 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 | Yes (21312 ÷ 12 = 1776) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 21312 a prime number?
No. 21312 = × × 37, so it is divisible by 2.
What are the factors of 21312?
1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 32, 36, 37, 48, 64, 72, 74, 96, 111, 144, 148, 192, 222, 288, 296, 333, 444, 576, 592, 666, 888, 1184, 1332, 1776, 2368, 2664, 3552, 5328, 7104, 10656, 21312.
What is 21312 in binary?
101001101000000 (hexadecimal 5340, octal 51500).
What is the square root of 21312?
About 145.9863, exactly 24√37.
Is 21312 divisible by 3?
Yes. Its digits add up to 9, a multiple of 3.
What is special about the number 21312?
21312 is a palindrome: it reads 21312 backwards too; a happy number: repeatedly adding the squares of its digits reaches 1; a Harshad number: divisible by its digit sum 9.