The number 13723
13723 is a twin prime (13721 and 13723 are both prime) and the 1624th prime number. Its only divisors are 1 and 13723.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 13723: a twin prime (13721 and 13723 are both prime); the 1624th prime number.
- 2
13723 is prime, so its only factors are 1 and 13723. It is the 1624th prime; the next prime is 13729 and the one before is 13721.
- 3
The divisors add up to 13724; without 13723 itself that is 1, so 13723 is deficient (1 is less than 13723). Euler's totient φ(13723) = 13722 numbers up to 13723 share no factor with it.
- 4
The digits of 13723 add up to 16, and repeating that until one digit is left gives the digital root 7. The Collatz sequence (halve if even, else 3n+1) takes 58 steps to reach 1.
13723 at a glance
| Property | Value |
|---|---|
| Type | prime |
| Number of divisors | 2 |
| Sum of divisors | 13724 |
| Euler totient φ(n) | 13722 |
| Square | 188320729 |
| Cube | 2584325364067 |
| Square root | 117.145209 |
| Digit sum / digital root | 16 / 7 |
| Collatz steps to 1 | 58 |
| Scientific notation | 1.3723 × |
13723 in other forms
| Form | Value |
|---|---|
| In words | thirteen thousand seven hundred and twenty-three |
| Binary (base 2) | 11010110011011 |
| Octal (base 8) | 32633 |
| Hexadecimal (base 16) | 359B |
| Base 3 | 200211021 |
| As time | 13723 seconds = 3 h 48 min 43 s |
Is 13723 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 3) | 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 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 3) | 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 6) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | No (remainder 7) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 13723 a prime number?
Yes. 13723 is divisible only by 1 and itself.
What are the factors of 13723?
1, 13723.
What is 13723 in binary?
11010110011011 (hexadecimal 359B, octal 32633).
What is the square root of 13723?
About 117.1452.
Is 13723 divisible by 3?
No. Its digits add up to 16, which is not a multiple of 3.
What is special about the number 13723?
13723 is a twin prime (13721 and 13723 are both prime); the 1624th prime number.