The number 9216
9216 is a perfect square (96²). Its prime factorisation is × . Divisors (33): 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 32, 36, 48, 64, 72 … 9216.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 9216: a perfect square (96²); a Harshad number: divisible by its digit sum 18.
- 2
9216 is composite. Its prime factorisation is
- 3
The divisors add up to 26611; without 9216 itself that is 17395, so 9216 is abundant (17395 is more than 9216). Euler's totient φ(9216) = 3072 numbers up to 9216 share no factor with it.
- 4
The digits of 9216 add up to 18, and repeating that until one digit is left gives the digital root 9. The Collatz sequence (halve if even, else 3n+1) takes 29 steps to reach 1.
LaTeX source of the formulas on this page
\[ 9216 = 2^{10} \times 3^{2} \]9216 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 33 |
| Sum of divisors | 26611 |
| Euler totient φ(n) | 3072 |
| Square | 84934656 |
| Cube | 782757789696 |
| Square root | 96 |
| Digit sum / digital root | 18 / 9 |
| Collatz steps to 1 | 29 |
| Scientific notation | 9.216 × |
| Perfect power |
9216 in other forms
| Form | Value |
|---|---|
| In words | nine thousand two hundred and sixteen |
| Binary (base 2) | 10010000000000 |
| Octal (base 8) | 22000 |
| Hexadecimal (base 16) | 2400 |
| Base 3 | 110122100 |
| As time | 9216 seconds = 2 h 33 min 36 s |
Is 9216 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (9216 ÷ 2 = 4608) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (9216 ÷ 3 = 3072) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (9216 ÷ 4 = 2304) | 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 (9216 ÷ 6 = 1536) | 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 (9216 ÷ 8 = 1152) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | Yes (9216 ÷ 9 = 1024) | 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 9) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (9216 ÷ 12 = 768) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 9216 a prime number?
No. 9216 = × , so it is divisible by 2.
What are the factors of 9216?
1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 32, 36, 48, 64, 72, 96, 128, 144, 192, 256, 288, 384, 512, 576, 768, 1024, 1152, 1536, 2304, 3072, 4608, 9216.
What is 9216 in binary?
10010000000000 (hexadecimal 2400, octal 22000).
What is the square root of 9216?
96, because 96 × 96 = 9216.
Is 9216 divisible by 3?
Yes. Its digits add up to 18, a multiple of 3.
What is special about the number 9216?
9216 is a perfect square (96²); a Harshad number: divisible by its digit sum 18.