The number 21013
21013 is a twin prime (21011 and 21013 are both prime) and the 2363rd prime number. Its only divisors are 1 and 21013.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 21013: a twin prime (21011 and 21013 are both prime); the 2363rd prime number.
- 2
21013 is prime, so its only factors are 1 and 21013. It is the 2363rd prime; the next prime is 21017 and the one before is 21011.
- 3
The divisors add up to 21014; without 21013 itself that is 1, so 21013 is deficient (1 is less than 21013). Euler's totient φ(21013) = 21012 numbers up to 21013 share no factor with it.
- 4
The digits of 21013 add up to 7, and repeating that until one digit is left gives the digital root 7. The Collatz sequence (halve if even, else 3n+1) takes 30 steps to reach 1.
21013 at a glance
| Property | Value |
|---|---|
| Type | prime |
| Number of divisors | 2 |
| Sum of divisors | 21014 |
| Euler totient φ(n) | 21012 |
| Square | 441546169 |
| Cube | 9278209649197 |
| Square root | 144.958615 |
| Digit sum / digital root | 7 / 7 |
| Collatz steps to 1 | 30 |
| Scientific notation | 2.1013 × |
21013 in other forms
| Form | Value |
|---|---|
| In words | twenty-one thousand and thirteen |
| Binary (base 2) | 101001000010101 |
| Octal (base 8) | 51025 |
| Hexadecimal (base 16) | 5215 |
| Base 3 | 1001211021 |
| As time | 21013 seconds = 5 h 50 min 13 s |
Is 21013 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 3) | 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 6) | 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 5) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 7) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | No (remainder 3) | 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 1) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 21013 a prime number?
Yes. 21013 is divisible only by 1 and itself.
What are the factors of 21013?
1, 21013.
What is 21013 in binary?
101001000010101 (hexadecimal 5215, octal 51025).
What is the square root of 21013?
About 144.9586.
Is 21013 divisible by 3?
No. Its digits add up to 7, which is not a multiple of 3.
What is special about the number 21013?
21013 is a twin prime (21011 and 21013 are both prime); the 2363rd prime number.