The number 16007
16007 is the 1864th prime number. Its only divisors are 1 and 16007.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 16007: the 1864th prime number; a happy number: repeatedly adding the squares of its digits reaches 1.
- 2
16007 is prime, so its only factors are 1 and 16007. It is the 1864th prime; the next prime is 16033 and the one before is 16001.
- 3
The divisors add up to 16008; without 16007 itself that is 1, so 16007 is deficient (1 is less than 16007). Euler's totient φ(16007) = 16006 numbers up to 16007 share no factor with it.
- 4
The digits of 16007 add up to 14, and repeating that until one digit is left gives the digital root 5. The Collatz sequence (halve if even, else 3n+1) takes 84 steps to reach 1.
16007 at a glance
| Property | Value |
|---|---|
| Type | prime |
| Number of divisors | 2 |
| Sum of divisors | 16008 |
| Euler totient φ(n) | 16006 |
| Square | 256224049 |
| Cube | 4101378352343 |
| Square root | 126.518773 |
| Digit sum / digital root | 14 / 5 |
| Collatz steps to 1 | 84 |
| Scientific notation | 1.6007 × |
16007 in other forms
| Form | Value |
|---|---|
| In words | sixteen thousand and seven |
| Binary (base 2) | 11111010000111 |
| Octal (base 8) | 37207 |
| Hexadecimal (base 16) | 3E87 |
| Base 3 | 210221212 |
| As time | 16007 seconds = 4 h 26 min 47 s |
Is 16007 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 2) | 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 5) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 5) | 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 5) | 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 2) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | No (remainder 11) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 16007 a prime number?
Yes. 16007 is divisible only by 1 and itself.
What are the factors of 16007?
1, 16007.
What is 16007 in binary?
11111010000111 (hexadecimal 3E87, octal 37207).
What is the square root of 16007?
About 126.5188.
Is 16007 divisible by 3?
No. Its digits add up to 14, which is not a multiple of 3.
What is special about the number 16007?
16007 is the 1864th prime number; a happy number: repeatedly adding the squares of its digits reaches 1.