The number 13721
13721 is a twin prime (13721 and 13723 are both prime) and the 1623rd prime number. Its only divisors are 1 and 13721.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 13721: a twin prime (13721 and 13723 are both prime); the 1623rd prime number.
- 2
13721 is prime, so its only factors are 1 and 13721. It is the 1623rd prime; the next prime is 13723 and the one before is 13711.
- 3
The divisors add up to 13722; without 13721 itself that is 1, so 13721 is deficient (1 is less than 13721). Euler's totient φ(13721) = 13720 numbers up to 13721 share no factor with it.
- 4
The digits of 13721 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 63 steps to reach 1.
13721 at a glance
| Property | Value |
|---|---|
| Type | prime |
| Number of divisors | 2 |
| Sum of divisors | 13722 |
| Euler totient φ(n) | 13720 |
| Square | 188265841 |
| Cube | 2583195604361 |
| Square root | 117.136672 |
| Digit sum / digital root | 14 / 5 |
| Collatz steps to 1 | 63 |
| Scientific notation | 1.3721 × |
13721 in other forms
| Form | Value |
|---|---|
| In words | thirteen thousand seven hundred and twenty-one |
| Binary (base 2) | 11010110011001 |
| Octal (base 8) | 32631 |
| Hexadecimal (base 16) | 3599 |
| Base 3 | 200211012 |
| As time | 13721 seconds = 3 h 48 min 41 s |
Is 13721 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 5) | 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 4) | 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 13721 a prime number?
Yes. 13721 is divisible only by 1 and itself.
What are the factors of 13721?
1, 13721.
What is 13721 in binary?
11010110011001 (hexadecimal 3599, octal 32631).
What is the square root of 13721?
About 117.1367.
Is 13721 divisible by 3?
No. Its digits add up to 14, which is not a multiple of 3.
What is special about the number 13721?
13721 is a twin prime (13721 and 13723 are both prime); the 1623rd prime number.