The number 13988
13988 is a composite number with 12 divisors. Its prime factorisation is × 13 × 269. Divisors (12): 1, 2, 4, 13, 26, 52, 269, 538, 1076, 3497, 6994, 13988.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 13988: a happy number: repeatedly adding the squares of its digits reaches 1.
- 2
13988 is composite. Its prime factorisation is
- 3
The divisors add up to 26460; without 13988 itself that is 12472, so 13988 is deficient (12472 is less than 13988). Euler's totient φ(13988) = 6432 numbers up to 13988 share no factor with it.
- 4
The digits of 13988 add up to 29, and repeating that until one digit is left gives the digital root 2. The Collatz sequence (halve if even, else 3n+1) takes 107 steps to reach 1.
LaTeX source of the formulas on this page
\[ 13988 = 2^{2} \times 13 \times 269 \]13988 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 12 |
| Sum of divisors | 26460 |
| Euler totient φ(n) | 6432 |
| Square | 195664144 |
| Cube | 2736950046272 |
| Square root | 118.270876 (= 2√3497) |
| Digit sum / digital root | 29 / 2 |
| Collatz steps to 1 | 107 |
| Scientific notation | 1.3988 × |
13988 in other forms
| Form | Value |
|---|---|
| In words | thirteen thousand nine hundred and eighty-eight |
| Binary (base 2) | 11011010100100 |
| Octal (base 8) | 33244 |
| Hexadecimal (base 16) | 36A4 |
| Base 3 | 201012002 |
| As time | 13988 seconds = 3 h 53 min 8 s |
Is 13988 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (13988 ÷ 2 = 6994) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | No (remainder 2) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (13988 ÷ 4 = 3497) | 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 2) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 2) | 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 4) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 2) | 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 7) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | No (remainder 8) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 13988 a prime number?
No. 13988 = × 13 × 269, so it is divisible by 2.
What are the factors of 13988?
1, 2, 4, 13, 26, 52, 269, 538, 1076, 3497, 6994, 13988.
What is 13988 in binary?
11011010100100 (hexadecimal 36A4, octal 33244).
What is the square root of 13988?
About 118.2709, exactly 2√3497.
Is 13988 divisible by 3?
No. Its digits add up to 29, which is not a multiple of 3.
What is special about the number 13988?
13988 is a happy number: repeatedly adding the squares of its digits reaches 1.