The number 16807
16807 is a perfect power (). Its prime factorisation is . Divisors (6): 1, 7, 49, 343, 2401, 16807.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 16807: a perfect power ().
- 2
16807 is composite. Its prime factorisation is
- 3
The divisors add up to 19608; without 16807 itself that is 2801, so 16807 is deficient (2801 is less than 16807). Euler's totient ฯ(16807) = 14406 numbers up to 16807 share no factor with it.
- 4
The digits of 16807 add up to 22, and repeating that until one digit is left gives the digital root 4. The Collatz sequence (halve if even, else 3n+1) takes 66 steps to reach 1.
LaTeX source of the formulas on this page
\[ 16807 = 7^{5} \]16807 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 6 |
| Sum of divisors | 19608 |
| Euler totient ฯ(n) | 14406 |
| Square | 282475249 |
| Cube | 4747561509943 |
| Square root | 129.641814 (= 49โ7) |
| Digit sum / digital root | 22 / 4 |
| Collatz steps to 1 | 66 |
| Scientific notation | 1.6807 ร |
| Perfect power |
16807 in other forms
| Form | Value |
|---|---|
| In words | sixteen thousand eight hundred and seven |
| Binary (base 2) | 100000110100111 |
| Octal (base 8) | 40647 |
| Hexadecimal (base 16) | 41A7 |
| Base 3 | 212001111 |
| As time | 16807 seconds = 4 h 40 min 7 s |
Is 16807 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 | No (remainder 1) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | No (remainder 3) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | No (remainder 2) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | No (remainder 1) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | Yes (16807 รท 7 = 2401) | 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 7) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 4) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | No (remainder 7) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 10) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | No (remainder 7) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 16807 a prime number?
No. 16807 = , so it is divisible by 7.
What are the factors of 16807?
1, 7, 49, 343, 2401, 16807.
What is 16807 in binary?
100000110100111 (hexadecimal 41A7, octal 40647).
What is the square root of 16807?
About 129.6418, exactly 49โ7.
Is 16807 divisible by 3?
No. Its digits add up to 22, which is not a multiple of 3.
What is special about the number 16807?
16807 is a perfect power ().