The number 13992
13992 is a composite number with 32 divisors. Its prime factorisation is × 3 × 11 × 53. Divisors (32): 1, 2, 3, 4, 6, 8, 11, 12, 22, 24, 33, 44, 53, 66, 88, 106 … 13992.
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How to work it out
- 1
What is special about 13992: a happy number: repeatedly adding the squares of its digits reaches 1; a Harshad number: divisible by its digit sum 24.
- 2
13992 is composite. Its prime factorisation is
- 3
The divisors add up to 38880; without 13992 itself that is 24888, so 13992 is abundant (24888 is more than 13992). Euler's totient φ(13992) = 4160 numbers up to 13992 share no factor with it.
- 4
The digits of 13992 add up to 24, and repeating that until one digit is left gives the digital root 6. The Collatz sequence (halve if even, else 3n+1) takes 120 steps to reach 1.
LaTeX source of the formulas on this page
\[ 13992 = 2^{3} \times 3 \times 11 \times 53 \]13992 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 32 |
| Sum of divisors | 38880 |
| Euler totient φ(n) | 4160 |
| Square | 195776064 |
| Cube | 2739298687488 |
| Square root | 118.287785 (= 2√3498) |
| Digit sum / digital root | 24 / 6 |
| Collatz steps to 1 | 120 |
| Scientific notation | 1.3992 × |
13992 in other forms
| Form | Value |
|---|---|
| In words | thirteen thousand nine hundred and ninety-two |
| Binary (base 2) | 11011010101000 |
| Octal (base 8) | 33250 |
| Hexadecimal (base 16) | 36A8 |
| Base 3 | 201012020 |
| As time | 13992 seconds = 3 h 53 min 12 s |
Is 13992 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (13992 ÷ 2 = 6996) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (13992 ÷ 3 = 4664) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (13992 ÷ 4 = 3498) | 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 (13992 ÷ 6 = 2332) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 6) | 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 (13992 ÷ 8 = 1749) | 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 | Yes (13992 ÷ 11 = 1272) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (13992 ÷ 12 = 1166) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 13992 a prime number?
No. 13992 = × 3 × 11 × 53, so it is divisible by 2.
What are the factors of 13992?
1, 2, 3, 4, 6, 8, 11, 12, 22, 24, 33, 44, 53, 66, 88, 106, 132, 159, 212, 264, 318, 424, 583, 636, 1166, 1272, 1749, 2332, 3498, 4664, 6996, 13992.
What is 13992 in binary?
11011010101000 (hexadecimal 36A8, octal 33250).
What is the square root of 13992?
About 118.2878, exactly 2√3498.
Is 13992 divisible by 3?
Yes. Its digits add up to 24, a multiple of 3.
What is special about the number 13992?
13992 is a happy number: repeatedly adding the squares of its digits reaches 1; a Harshad number: divisible by its digit sum 24.