The number 13888
13888 is a composite number with 28 divisors. Its prime factorisation is × 7 × 31. Divisors (28): 1, 2, 4, 7, 8, 14, 16, 28, 31, 32, 56, 62, 64, 112, 124, 217 … 13888.
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How to work it out
- 1
What is special about 13888: a Harshad number: divisible by its digit sum 28.
- 2
13888 is composite. Its prime factorisation is
- 3
The divisors add up to 32512; without 13888 itself that is 18624, so 13888 is abundant (18624 is more than 13888). Euler's totient φ(13888) = 5760 numbers up to 13888 share no factor with it.
- 4
The digits of 13888 add up to 28, and repeating that until one digit is left gives the digital root 1. The Collatz sequence (halve if even, else 3n+1) takes 32 steps to reach 1.
LaTeX source of the formulas on this page
\[ 13888 = 2^{6} \times 7 \times 31 \]13888 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 28 |
| Sum of divisors | 32512 |
| Euler totient φ(n) | 5760 |
| Square | 192876544 |
| Cube | 2678669443072 |
| Square root | 117.847359 (= 8√217) |
| Digit sum / digital root | 28 / 1 |
| Collatz steps to 1 | 32 |
| Scientific notation | 1.3888 × |
13888 in other forms
| Form | Value |
|---|---|
| In words | thirteen thousand eight hundred and eighty-eight |
| Binary (base 2) | 11011001000000 |
| Octal (base 8) | 33100 |
| Hexadecimal (base 16) | 3640 |
| Base 3 | 201001101 |
| As time | 13888 seconds = 3 h 51 min 28 s |
Is 13888 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (13888 ÷ 2 = 6944) | 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 | Yes (13888 ÷ 4 = 3472) | 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 4) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | Yes (13888 ÷ 7 = 1984) | 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 | Yes (13888 ÷ 8 = 1736) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 1) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | No (remainder 8) | 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 4) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 13888 a prime number?
No. 13888 = × 7 × 31, so it is divisible by 2.
What are the factors of 13888?
1, 2, 4, 7, 8, 14, 16, 28, 31, 32, 56, 62, 64, 112, 124, 217, 224, 248, 434, 448, 496, 868, 992, 1736, 1984, 3472, 6944, 13888.
What is 13888 in binary?
11011001000000 (hexadecimal 3640, octal 33100).
What is the square root of 13888?
About 117.8474, exactly 8√217.
Is 13888 divisible by 3?
No. Its digits add up to 28, which is not a multiple of 3.
What is special about the number 13888?
13888 is a Harshad number: divisible by its digit sum 28.