The number 13842
13842 is a composite number with 12 divisors. Its prime factorisation is 2 × × 769. Divisors (12): 1, 2, 3, 6, 9, 18, 769, 1538, 2307, 4614, 6921, 13842.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 13842: a happy number: repeatedly adding the squares of its digits reaches 1; a Harshad number: divisible by its digit sum 18.
- 2
13842 is composite. Its prime factorisation is
- 3
The divisors add up to 30030; without 13842 itself that is 16188, so 13842 is abundant (16188 is more than 13842). Euler's totient φ(13842) = 4608 numbers up to 13842 share no factor with it.
- 4
The digits of 13842 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
\[ 13842 = 2 \times 3^{2} \times 769 \]13842 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 12 |
| Sum of divisors | 30030 |
| Euler totient φ(n) | 4608 |
| Square | 191600964 |
| Cube | 2652140543688 |
| Square root | 117.652029 (= 3√1538) |
| Digit sum / digital root | 18 / 9 |
| Collatz steps to 1 | 76 |
| Scientific notation | 1.3842 × |
13842 in other forms
| Form | Value |
|---|---|
| In words | thirteen thousand eight hundred and forty-two |
| Binary (base 2) | 11011000010010 |
| Octal (base 8) | 33022 |
| Hexadecimal (base 16) | 3612 |
| Base 3 | 200222200 |
| As time | 13842 seconds = 3 h 50 min 42 s |
Is 13842 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (13842 ÷ 2 = 6921) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (13842 ÷ 3 = 4614) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | No (remainder 2) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | No (remainder 2) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (13842 ÷ 6 = 2307) | 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 2) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | Yes (13842 ÷ 9 = 1538) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | No (remainder 2) | 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 6) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 13842 a prime number?
No. 13842 = 2 × × 769, so it is divisible by 2.
What are the factors of 13842?
1, 2, 3, 6, 9, 18, 769, 1538, 2307, 4614, 6921, 13842.
What is 13842 in binary?
11011000010010 (hexadecimal 3612, octal 33022).
What is the square root of 13842?
About 117.6520, exactly 3√1538.
Is 13842 divisible by 3?
Yes. Its digits add up to 18, a multiple of 3.
What is special about the number 13842?
13842 is a happy number: repeatedly adding the squares of its digits reaches 1; a Harshad number: divisible by its digit sum 18.