The number 13851
13851 is a binary palindrome (11011000011011). Its prime factorisation is × 19. Divisors (14): 1, 3, 9, 19, 27, 57, 81, 171, 243, 513, 729, 1539, 4617, 13851.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 13851: a binary palindrome (11011000011011); a happy number: repeatedly adding the squares of its digits reaches 1.
- 2
13851 is composite. Its prime factorisation is
- 3
The divisors add up to 21860; without 13851 itself that is 8009, so 13851 is deficient (8009 is less than 13851). Euler's totient φ(13851) = 8748 numbers up to 13851 share no factor with it.
- 4
The digits of 13851 add up to 18, and repeating that until one digit is left gives the digital root 9. The Collatz sequence (halve if even, else 3n+1) takes 76 steps to reach 1.
LaTeX source of the formulas on this page
\[ 13851 = 3^{6} \times 19 \]13851 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 14 |
| Sum of divisors | 21860 |
| Euler totient φ(n) | 8748 |
| Square | 191850201 |
| Cube | 2657317134051 |
| Square root | 117.690271 (= 27√19) |
| Digit sum / digital root | 18 / 9 |
| Collatz steps to 1 | 76 |
| Scientific notation | 1.3851 × |
13851 in other forms
| Form | Value |
|---|---|
| In words | thirteen thousand eight hundred and fifty-one |
| Binary (base 2) | 11011000011011 |
| Octal (base 8) | 33033 |
| Hexadecimal (base 16) | 361B |
| Base 3 | 201000000 |
| As time | 13851 seconds = 3 h 50 min 51 s |
Is 13851 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 | Yes (13851 ÷ 3 = 4617) | 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 1) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | No (remainder 3) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 5) | 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 | Yes (13851 ÷ 9 = 1539) | 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 3) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 13851 a prime number?
No. 13851 = × 19, so it is divisible by 3.
What are the factors of 13851?
1, 3, 9, 19, 27, 57, 81, 171, 243, 513, 729, 1539, 4617, 13851.
What is 13851 in binary?
11011000011011 (hexadecimal 361B, octal 33033).
What is the square root of 13851?
About 117.6903, exactly 27√19.
Is 13851 divisible by 3?
Yes. Its digits add up to 18, a multiple of 3.
What is special about the number 13851?
13851 is a binary palindrome (11011000011011); a happy number: repeatedly adding the squares of its digits reaches 1.