The number 7001
7001 is the 901st prime number. Its only divisors are 1 and 7001.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 7001: the 901st prime number.
- 2
7001 is prime, so its only factors are 1 and 7001. It is the 901st prime; the next prime is 7013 and the one before is 6997.
- 3
The divisors add up to 7002; without 7001 itself that is 1, so 7001 is deficient (1 is less than 7001). Euler's totient φ(7001) = 7000 numbers up to 7001 share no factor with it.
- 4
The digits of 7001 add up to 8, and repeating that until one digit is left gives the digital root 8. The Collatz sequence (halve if even, else 3n+1) takes 31 steps to reach 1.
7001 at a glance
| Property | Value |
|---|---|
| Type | prime |
| Number of divisors | 2 |
| Sum of divisors | 7002 |
| Euler totient φ(n) | 7000 |
| Square | 49014001 |
| Cube | 343147021001 |
| Square root | 83.671979 |
| Digit sum / digital root | 8 / 8 |
| Collatz steps to 1 | 31 |
| Scientific notation | 7.001 × |
7001 in other forms
| Form | Value |
|---|---|
| In words | seven thousand and one |
| Binary (base 2) | 1101101011001 |
| Octal (base 8) | 15531 |
| Hexadecimal (base 16) | 1B59 |
| Base 3 | 100121022 |
| As time | 7001 seconds = 1 h 56 min 41 s |
Is 7001 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 1) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | No (remainder 1) | 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 1) | 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 | No (remainder 8) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | No (remainder 1) | 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 5) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 7001 a prime number?
Yes. 7001 is divisible only by 1 and itself.
What are the factors of 7001?
1, 7001.
What is 7001 in binary?
1101101011001 (hexadecimal 1B59, octal 15531).
What is the square root of 7001?
About 83.6720.
Is 7001 divisible by 3?
No. Its digits add up to 8, which is not a multiple of 3.
What is special about the number 7001?
7001 is the 901st prime number.