The number 21609
21609 is a perfect square (147²). Its prime factorisation is × . Divisors (15): 1, 3, 7, 9, 21, 49, 63, 147, 343, 441, 1029, 2401, 3087, 7203, 21609.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 21609: a perfect square (147²).
- 2
21609 is composite. Its prime factorisation is
- 3
The divisors add up to 36413; without 21609 itself that is 14804, so 21609 is deficient (14804 is less than 21609). Euler's totient φ(21609) = 12348 numbers up to 21609 share no factor with it.
- 4
The digits of 21609 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 193 steps to reach 1.
LaTeX source of the formulas on this page
\[ 21609 = 3^{2} \times 7^{4} \]21609 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 15 |
| Sum of divisors | 36413 |
| Euler totient φ(n) | 12348 |
| Square | 466948881 |
| Cube | 10090298369529 |
| Square root | 147 |
| Digit sum / digital root | 18 / 9 |
| Collatz steps to 1 | 193 |
| Scientific notation | 2.1609 × |
| Perfect power |
21609 in other forms
| Form | Value |
|---|---|
| In words | twenty-one thousand six hundred and nine |
| Binary (base 2) | 101010001101001 |
| Octal (base 8) | 52151 |
| Hexadecimal (base 16) | 5469 |
| Base 3 | 1002122100 |
| As time | 21609 seconds = 6 h 0 min 9 s |
Is 21609 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 (21609 ÷ 3 = 7203) | 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 | Yes (21609 ÷ 7 = 3087) | 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 (21609 ÷ 9 = 2401) | 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 | No (remainder 5) | 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 21609 a prime number?
No. 21609 = × , so it is divisible by 3.
What are the factors of 21609?
1, 3, 7, 9, 21, 49, 63, 147, 343, 441, 1029, 2401, 3087, 7203, 21609.
What is 21609 in binary?
101010001101001 (hexadecimal 5469, octal 52151).
What is the square root of 21609?
147, because 147 × 147 = 21609.
Is 21609 divisible by 3?
Yes. Its digits add up to 18, a multiple of 3.
What is special about the number 21609?
21609 is a perfect square (147²).