The number 88209
88209 is a perfect square (297²). Its prime factorisation is × . Divisors (21): 1, 3, 9, 11, 27, 33, 81, 99, 121, 243, 297, 363, 729, 891, 1089, 2673 … 88209.
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How to work it out
- 1
What is special about 88209: a perfect square (297²); a Harshad number: divisible by its digit sum 27.
- 2
88209 is composite. Its prime factorisation is
- 3
The divisors add up to 145369; without 88209 itself that is 57160, so 88209 is deficient (57160 is less than 88209). Euler's totient φ(88209) = 53460 numbers up to 88209 share no factor with it.
- 4
The digits of 88209 add up to 27, and repeating that until one digit is left gives the digital root 9. The Collatz sequence (halve if even, else 3n+1) takes 146 steps to reach 1.
LaTeX source of the formulas on this page
\[ 88209 = 3^{6} \times 11^{2} \]88209 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 21 |
| Sum of divisors | 145369 |
| Euler totient φ(n) | 53460 |
| Square | 7780827681 |
| Cube | 686339028913329 |
| Square root | 297 |
| Digit sum / digital root | 27 / 9 |
| Collatz steps to 1 | 146 |
| Scientific notation | 8.8209 × |
| Perfect power |
88209 in other forms
| Form | Value |
|---|---|
| In words | eighty-eight thousand two hundred and nine |
| Binary (base 2) | 10101100010010001 |
| Octal (base 8) | 254221 |
| Hexadecimal (base 16) | 15891 |
| Base 3 | 11111000000 |
| As time | 88209 seconds = 24 h 30 min 9 s |
Is 88209 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | No (remainder 1) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (88209 ÷ 3 = 29403) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | No (remainder 1) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | No (remainder 4) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | No (remainder 3) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 2) | 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 | No (remainder 1) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | Yes (88209 ÷ 9 = 9801) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | No (remainder 9) | A number is divisible by 10 if the last digit is 0. |
| 11 | Yes (88209 ÷ 11 = 8019) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | No (remainder 9) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 88209 a prime number?
No. 88209 = × , so it is divisible by 3.
What are the factors of 88209?
1, 3, 9, 11, 27, 33, 81, 99, 121, 243, 297, 363, 729, 891, 1089, 2673, 3267, 8019, 9801, 29403, 88209.
What is 88209 in binary?
10101100010010001 (hexadecimal 15891, octal 254221).
What is the square root of 88209?
297, because 297 × 297 = 88209.
Is 88209 divisible by 3?
Yes. Its digits add up to 27, a multiple of 3.
What is special about the number 88209?
88209 is a perfect square (297²); a Harshad number: divisible by its digit sum 27.