The number 21216
21216 is a composite number with 48 divisors. Its prime factorisation is × 3 × 13 × 17. Divisors (48): 1, 2, 3, 4, 6, 8, 12, 13, 16, 17, 24, 26, 32, 34, 39, 48 … 21216.
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How to work it out
- 1
What is special about 21216: a Harshad number: divisible by its digit sum 12.
- 2
21216 is composite. Its prime factorisation is
- 3
The divisors add up to 63504; without 21216 itself that is 42288, so 21216 is abundant (42288 is more than 21216). Euler's totient φ(21216) = 6144 numbers up to 21216 share no factor with it.
- 4
The digits of 21216 add up to 12, and repeating that until one digit is left gives the digital root 3. The Collatz sequence (halve if even, else 3n+1) takes 30 steps to reach 1.
LaTeX source of the formulas on this page
\[ 21216 = 2^{5} \times 3 \times 13 \times 17 \]21216 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 48 |
| Sum of divisors | 63504 |
| Euler totient φ(n) | 6144 |
| Square | 450118656 |
| Cube | 9549717405696 |
| Square root | 145.657132 (= 4√1326) |
| Digit sum / digital root | 12 / 3 |
| Collatz steps to 1 | 30 |
| Scientific notation | 2.1216 × |
21216 in other forms
| Form | Value |
|---|---|
| In words | twenty-one thousand two hundred and sixteen |
| Binary (base 2) | 101001011100000 |
| Octal (base 8) | 51340 |
| Hexadecimal (base 16) | 52E0 |
| Base 3 | 1002002210 |
| As time | 21216 seconds = 5 h 53 min 36 s |
Is 21216 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (21216 ÷ 2 = 10608) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (21216 ÷ 3 = 7072) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (21216 ÷ 4 = 5304) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | No (remainder 1) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (21216 ÷ 6 = 3536) | 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 (21216 ÷ 8 = 2652) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 3) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | No (remainder 6) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 8) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (21216 ÷ 12 = 1768) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 21216 a prime number?
No. 21216 = × 3 × 13 × 17, so it is divisible by 2.
What are the factors of 21216?
1, 2, 3, 4, 6, 8, 12, 13, 16, 17, 24, 26, 32, 34, 39, 48, 51, 52, 68, 78, 96, 102, 104, 136, 156, 204, 208, 221, 272, 312, 408, 416, 442, 544, 624, 663, 816, 884, 1248, 1326, 1632, 1768, 2652, 3536, 5304, 7072, 10608, 21216.
What is 21216 in binary?
101001011100000 (hexadecimal 52E0, octal 51340).
What is the square root of 21216?
About 145.6571, exactly 4√1326.
Is 21216 divisible by 3?
Yes. Its digits add up to 12, a multiple of 3.
What is special about the number 21216?
21216 is a Harshad number: divisible by its digit sum 12.