The number 14688
14688 is a composite number with 48 divisors. Its prime factorisation is × × 17. Divisors (48): 1, 2, 3, 4, 6, 8, 9, 12, 16, 17, 18, 24, 27, 32, 34, 36 … 14688.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 14688: a Harshad number: divisible by its digit sum 27.
- 2
14688 is composite. Its prime factorisation is
- 3
The divisors add up to 45360; without 14688 itself that is 30672, so 14688 is abundant (30672 is more than 14688). Euler's totient φ(14688) = 4608 numbers up to 14688 share no factor with it.
- 4
The digits of 14688 add up to 27, and repeating that until one digit is left gives the digital root 9. The Collatz sequence (halve if even, else 3n+1) takes 133 steps to reach 1.
LaTeX source of the formulas on this page
\[ 14688 = 2^{5} \times 3^{3} \times 17 \]14688 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 48 |
| Sum of divisors | 45360 |
| Euler totient φ(n) | 4608 |
| Square | 215737344 |
| Cube | 3168750108672 |
| Square root | 121.194059 (= 12√102) |
| Digit sum / digital root | 27 / 9 |
| Collatz steps to 1 | 133 |
| Scientific notation | 1.4688 × |
14688 in other forms
| Form | Value |
|---|---|
| In words | fourteen thousand six hundred and eighty-eight |
| Binary (base 2) | 11100101100000 |
| Octal (base 8) | 34540 |
| Hexadecimal (base 16) | 3960 |
| Base 3 | 202011000 |
| As time | 14688 seconds = 4 h 4 min 48 s |
Is 14688 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (14688 ÷ 2 = 7344) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (14688 ÷ 3 = 4896) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (14688 ÷ 4 = 3672) | 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 (14688 ÷ 6 = 2448) | 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 | Yes (14688 ÷ 8 = 1836) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | Yes (14688 ÷ 9 = 1632) | 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 3) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (14688 ÷ 12 = 1224) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 14688 a prime number?
No. 14688 = × × 17, so it is divisible by 2.
What are the factors of 14688?
1, 2, 3, 4, 6, 8, 9, 12, 16, 17, 18, 24, 27, 32, 34, 36, 48, 51, 54, 68, 72, 96, 102, 108, 136, 144, 153, 204, 216, 272, 288, 306, 408, 432, 459, 544, 612, 816, 864, 918, 1224, 1632, 1836, 2448, 3672, 4896, 7344, 14688.
What is 14688 in binary?
11100101100000 (hexadecimal 3960, octal 34540).
What is the square root of 14688?
About 121.1941, exactly 12√102.
Is 14688 divisible by 3?
Yes. Its digits add up to 27, a multiple of 3.
What is special about the number 14688?
14688 is a Harshad number: divisible by its digit sum 27.