The number 216
216 is a perfect cube (). Its prime factorisation is × . Divisors (16): 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 27, 36, 54, 72, 108, 216.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 216: a perfect cube (); a Harshad number: divisible by its digit sum 9.
- 2
216 is composite. Its prime factorisation is
- 3
The divisors add up to 600; without 216 itself that is 384, so 216 is abundant (384 is more than 216). Euler's totient φ(216) = 72 numbers up to 216 share no factor with it.
- 4
The digits of 216 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 114 steps to reach 1.
LaTeX source of the formulas on this page
\[ 216 = 2^{3} \times 3^{3} \]216 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 16 |
| Sum of divisors | 600 |
| Euler totient φ(n) | 72 |
| Square | 46656 |
| Cube | 10077696 |
| Square root | 14.696938 (= 6√6) |
| Digit sum / digital root | 9 / 9 |
| Collatz steps to 1 | 114 |
| Scientific notation | 2.16 × |
| Perfect power |
216 in other forms
| Form | Value |
|---|---|
| In words | two hundred and sixteen |
| Roman numerals | CCXVI |
| Binary (base 2) | 11011000 |
| Octal (base 8) | 330 |
| Hexadecimal (base 16) | D8 |
| Base 3 | 22000 |
| As time | 216 seconds = 3 min 36 s |
Is 216 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (216 ÷ 2 = 108) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (216 ÷ 3 = 72) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (216 ÷ 4 = 54) | 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 (216 ÷ 6 = 36) | 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 (216 ÷ 8 = 27) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | Yes (216 ÷ 9 = 24) | 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 7) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (216 ÷ 12 = 18) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 216 a prime number?
No. 216 = × , so it is divisible by 2.
What are the factors of 216?
1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 27, 36, 54, 72, 108, 216.
What is 216 in binary?
11011000 (hexadecimal D8, octal 330).
What is the square root of 216?
About 14.6969, exactly 6√6.
What is 216 in Roman numerals?
CCXVI.
Is 216 divisible by 3?
Yes. Its digits add up to 9, a multiple of 3.
What is special about the number 216?
216 is a perfect cube (); a Harshad number: divisible by its digit sum 9.