The number 21001
21001 is the 2361st prime number. Its only divisors are 1 and 21001.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 21001: the 2361st prime number.
- 2
21001 is prime, so its only factors are 1 and 21001. It is the 2361st prime; the next prime is 21011 and the one before is 20983.
- 3
The divisors add up to 21002; without 21001 itself that is 1, so 21001 is deficient (1 is less than 21001). Euler's totient φ(21001) = 21000 numbers up to 21001 share no factor with it.
- 4
The digits of 21001 add up to 4, and repeating that until one digit is left gives the digital root 4. The Collatz sequence (halve if even, else 3n+1) takes 149 steps to reach 1.
21001 at a glance
| Property | Value |
|---|---|
| Type | prime |
| Number of divisors | 2 |
| Sum of divisors | 21002 |
| Euler totient φ(n) | 21000 |
| Square | 441042001 |
| Cube | 9262323063001 |
| Square root | 144.917218 |
| Digit sum / digital root | 4 / 4 |
| Collatz steps to 1 | 149 |
| Scientific notation | 2.1001 × |
21001 in other forms
| Form | Value |
|---|---|
| In words | twenty-one thousand and one |
| Binary (base 2) | 101001000001001 |
| Octal (base 8) | 51011 |
| Hexadecimal (base 16) | 5209 |
| Base 3 | 1001210211 |
| As time | 21001 seconds = 5 h 50 min 1 s |
Is 21001 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 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 1) | 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 4) | 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 2) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | No (remainder 1) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 21001 a prime number?
Yes. 21001 is divisible only by 1 and itself.
What are the factors of 21001?
1, 21001.
What is 21001 in binary?
101001000001001 (hexadecimal 5209, octal 51011).
What is the square root of 21001?
About 144.9172.
Is 21001 divisible by 3?
No. Its digits add up to 4, which is not a multiple of 3.
What is special about the number 21001?
21001 is the 2361st prime number.