The number 13902
13902 is a composite number with 16 divisors. Its prime factorisation is 2 × 3 × 7 × 331. Divisors (16): 1, 2, 3, 6, 7, 14, 21, 42, 331, 662, 993, 1986, 2317, 4634, 6951, 13902.
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How to work it out
- 1
13902 has no famous special property in the usual lists (prime, square, cube, triangular, Fibonacci, palindrome, perfect), but it is still a composite number.
- 2
13902 is composite. Its prime factorisation is
- 3
The divisors add up to 31872; without 13902 itself that is 17970, so 13902 is abundant (17970 is more than 13902). Euler's totient φ(13902) = 3960 numbers up to 13902 share no factor with it.
- 4
The digits of 13902 add up to 15, and repeating that until one digit is left gives the digital root 6. The Collatz sequence (halve if even, else 3n+1) takes 112 steps to reach 1.
LaTeX source of the formulas on this page
\[ 13902 = 2 \times 3 \times 7 \times 331 \]
13902 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 16 |
| Sum of divisors | 31872 |
| Euler totient φ(n) | 3960 |
| Square | 193265604 |
| Cube | 2686778426808 |
| Square root | 117.906743 |
| Digit sum / digital root | 15 / 6 |
| Collatz steps to 1 | 112 |
| Scientific notation | 1.3902 × |
13902 in other forms
| Form | Value |
|---|---|
| In words | thirteen thousand nine hundred and two |
| Binary (base 2) | 11011001001110 |
| Octal (base 8) | 33116 |
| Hexadecimal (base 16) | 364E |
| Base 3 | 201001220 |
| As time | 13902 seconds = 3 h 51 min 42 s |
Is 13902 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (13902 ÷ 2 = 6951) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (13902 ÷ 3 = 4634) | 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 (13902 ÷ 6 = 2317) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | Yes (13902 ÷ 7 = 1986) | 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 6) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 6) | 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 9) | 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 13902 a prime number?
No. 13902 = 2 × 3 × 7 × 331, so it is divisible by 2.
What are the factors of 13902?
1, 2, 3, 6, 7, 14, 21, 42, 331, 662, 993, 1986, 2317, 4634, 6951, 13902.
What is 13902 in binary?
11011001001110 (hexadecimal 364E, octal 33116).
What is the square root of 13902?
About 117.9067.
Is 13902 divisible by 3?
Yes. Its digits add up to 15, a multiple of 3.
What is special about the number 13902?
It is a composite number with 16 divisors.