The number 4007
4007 is the 553rd prime number. Its only divisors are 1 and 4007.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 4007: the 553rd prime number.
- 2
4007 is prime, so its only factors are 1 and 4007. It is the 553rd prime; the next prime is 4013 and the one before is 4003.
- 3
The divisors add up to 4008; without 4007 itself that is 1, so 4007 is deficient (1 is less than 4007). Euler's totient φ(4007) = 4006 numbers up to 4007 share no factor with it.
- 4
The digits of 4007 add up to 11, and repeating that until one digit is left gives the digital root 2. The Collatz sequence (halve if even, else 3n+1) takes 43 steps to reach 1.
4007 at a glance
| Property | Value |
|---|---|
| Type | prime |
| Number of divisors | 2 |
| Sum of divisors | 4008 |
| Euler totient φ(n) | 4006 |
| Square | 16056049 |
| Cube | 64336588343 |
| Square root | 63.300869 |
| Digit sum / digital root | 11 / 2 |
| Collatz steps to 1 | 43 |
| Scientific notation | 4.007 × |
4007 in other forms
| Form | Value |
|---|---|
| In words | four thousand and seven |
| Binary (base 2) | 111110100111 |
| Octal (base 8) | 7647 |
| Hexadecimal (base 16) | FA7 |
| Base 3 | 12111102 |
| As time | 4007 seconds = 1 h 6 min 47 s |
Is 4007 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 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 | No (remainder 7) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 2) | 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 3) | 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 4007 a prime number?
Yes. 4007 is divisible only by 1 and itself.
What are the factors of 4007?
1, 4007.
What is 4007 in binary?
111110100111 (hexadecimal FA7, octal 7647).
What is the square root of 4007?
About 63.3009.
Is 4007 divisible by 3?
No. Its digits add up to 11, which is not a multiple of 3.
What is special about the number 4007?
4007 is the 553rd prime number.