The number 13998
13998 is a composite number with 8 divisors. Its prime factorisation is 2 × 3 × 2333. Divisors (8): 1, 2, 3, 6, 2333, 4666, 6999, 13998.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 13998: a happy number: repeatedly adding the squares of its digits reaches 1.
- 2
13998 is composite. Its prime factorisation is
- 3
The divisors add up to 28008; without 13998 itself that is 14010, so 13998 is abundant (14010 is more than 13998). Euler's totient φ(13998) = 4664 numbers up to 13998 share no factor with it.
- 4
The digits of 13998 add up to 30, and repeating that until one digit is left gives the digital root 3. The Collatz sequence (halve if even, else 3n+1) takes 133 steps to reach 1.
LaTeX source of the formulas on this page
\[ 13998 = 2 \times 3 \times 2333 \]
13998 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 8 |
| Sum of divisors | 28008 |
| Euler totient φ(n) | 4664 |
| Square | 195944004 |
| Cube | 2742824167992 |
| Square root | 118.313144 |
| Digit sum / digital root | 30 / 3 |
| Collatz steps to 1 | 133 |
| Scientific notation | 1.3998 × |
13998 in other forms
| Form | Value |
|---|---|
| In words | thirteen thousand nine hundred and ninety-eight |
| Binary (base 2) | 11011010101110 |
| Octal (base 8) | 33256 |
| Hexadecimal (base 16) | 36AE |
| Base 3 | 201012110 |
| As time | 13998 seconds = 3 h 53 min 18 s |
Is 13998 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (13998 ÷ 2 = 6999) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (13998 ÷ 3 = 4666) | 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 3) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (13998 ÷ 6 = 2333) | 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 6) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 3) | 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 6) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 13998 a prime number?
No. 13998 = 2 × 3 × 2333, so it is divisible by 2.
What are the factors of 13998?
1, 2, 3, 6, 2333, 4666, 6999, 13998.
What is 13998 in binary?
11011010101110 (hexadecimal 36AE, octal 33256).
What is the square root of 13998?
About 118.3131.
Is 13998 divisible by 3?
Yes. Its digits add up to 30, a multiple of 3.
What is special about the number 13998?
13998 is a happy number: repeatedly adding the squares of its digits reaches 1.