The number 13873
13873 is the 1638th prime number. Its only divisors are 1 and 13873.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 13873: the 1638th prime number.
- 2
13873 is prime, so its only factors are 1 and 13873. It is the 1638th prime; the next prime is 13877 and the one before is 13859.
- 3
The divisors add up to 13874; without 13873 itself that is 1, so 13873 is deficient (1 is less than 13873). Euler's totient φ(13873) = 13872 numbers up to 13873 share no factor with it.
- 4
The digits of 13873 add up to 22, and repeating that until one digit is left gives the digital root 4. The Collatz sequence (halve if even, else 3n+1) takes 182 steps to reach 1.
13873 at a glance
| Property | Value |
|---|---|
| Type | prime |
| Number of divisors | 2 |
| Sum of divisors | 13874 |
| Euler totient φ(n) | 13872 |
| Square | 192460129 |
| Cube | 2669999369617 |
| Square root | 117.783700 |
| Digit sum / digital root | 22 / 4 |
| Collatz steps to 1 | 182 |
| Scientific notation | 1.3873 × |
13873 in other forms
| Form | Value |
|---|---|
| In words | thirteen thousand eight hundred and seventy-three |
| Binary (base 2) | 11011000110001 |
| Octal (base 8) | 33061 |
| Hexadecimal (base 16) | 3631 |
| Base 3 | 201000211 |
| As time | 13873 seconds = 3 h 51 min 13 s |
Is 13873 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 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 3) | 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 13873 a prime number?
Yes. 13873 is divisible only by 1 and itself.
What are the factors of 13873?
1, 13873.
What is 13873 in binary?
11011000110001 (hexadecimal 3631, octal 33061).
What is the square root of 13873?
About 117.7837.
Is 13873 divisible by 3?
No. Its digits add up to 22, which is not a multiple of 3.
What is special about the number 13873?
13873 is the 1638th prime number.