The number 17216
17216 is a composite number with 14 divisors. Its prime factorisation is × 269. Divisors (14): 1, 2, 4, 8, 16, 32, 64, 269, 538, 1076, 2152, 4304, 8608, 17216.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 17216: a happy number: repeatedly adding the squares of its digits reaches 1.
- 2
17216 is composite. Its prime factorisation is
- 3
The divisors add up to 34290; without 17216 itself that is 17074, so 17216 is deficient (17074 is less than 17216). Euler's totient φ(17216) = 8576 numbers up to 17216 share no factor with it.
- 4
The digits of 17216 add up to 17, and repeating that until one digit is left gives the digital root 8. The Collatz sequence (halve if even, else 3n+1) takes 35 steps to reach 1.
LaTeX source of the formulas on this page
\[ 17216 = 2^{6} \times 269 \]17216 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 14 |
| Sum of divisors | 34290 |
| Euler totient φ(n) | 8576 |
| Square | 296390656 |
| Cube | 5102661533696 |
| Square root | 131.209756 (= 8√269) |
| Digit sum / digital root | 17 / 8 |
| Collatz steps to 1 | 35 |
| Scientific notation | 1.7216 × |
17216 in other forms
| Form | Value |
|---|---|
| In words | seventeen thousand two hundred and sixteen |
| Binary (base 2) | 100001101000000 |
| Octal (base 8) | 41500 |
| Hexadecimal (base 16) | 4340 |
| Base 3 | 212121122 |
| As time | 17216 seconds = 4 h 46 min 56 s |
Is 17216 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (17216 ÷ 2 = 8608) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | No (remainder 2) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (17216 ÷ 4 = 4304) | 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 | No (remainder 2) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 3) | 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 (17216 ÷ 8 = 2152) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 8) | 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 1) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | No (remainder 8) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 17216 a prime number?
No. 17216 = × 269, so it is divisible by 2.
What are the factors of 17216?
1, 2, 4, 8, 16, 32, 64, 269, 538, 1076, 2152, 4304, 8608, 17216.
What is 17216 in binary?
100001101000000 (hexadecimal 4340, octal 41500).
What is the square root of 17216?
About 131.2098, exactly 8√269.
Is 17216 divisible by 3?
No. Its digits add up to 17, which is not a multiple of 3.
What is special about the number 17216?
17216 is a happy number: repeatedly adding the squares of its digits reaches 1.