The number 1728
1728 is a perfect cube (). Its prime factorisation is × . Divisors (28): 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 27, 32, 36, 48, 54 … 1728.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 1728: a perfect cube (); a Harshad number: divisible by its digit sum 18.
- 2
1728 is composite. Its prime factorisation is
- 3
The divisors add up to 5080; without 1728 itself that is 3352, so 1728 is abundant (3352 is more than 1728). Euler's totient φ(1728) = 576 numbers up to 1728 share no factor with it.
- 4
The digits of 1728 add up to 18, and repeating that until one digit is left gives the digital root 9. The Collatz sequence (halve if even, else 3n+1) takes 117 steps to reach 1.
LaTeX source of the formulas on this page
\[ 1728 = 2^{6} \times 3^{3} \]1728 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 28 |
| Sum of divisors | 5080 |
| Euler totient φ(n) | 576 |
| Square | 2985984 |
| Cube | 5159780352 |
| Square root | 41.569219 (= 24√3) |
| Digit sum / digital root | 18 / 9 |
| Collatz steps to 1 | 117 |
| Scientific notation | 1.728 × |
| Perfect power |
1728 in other forms
| Form | Value |
|---|---|
| In words | one thousand seven hundred and twenty-eight |
| Roman numerals | MDCCXXVIII |
| Binary (base 2) | 11011000000 |
| Octal (base 8) | 3300 |
| Hexadecimal (base 16) | 6C0 |
| Base 3 | 2101000 |
| As time | 1728 seconds = 28 min 48 s |
Is 1728 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (1728 ÷ 2 = 864) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (1728 ÷ 3 = 576) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (1728 ÷ 4 = 432) | 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 (1728 ÷ 6 = 288) | 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 (1728 ÷ 8 = 216) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | Yes (1728 ÷ 9 = 192) | 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 1) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (1728 ÷ 12 = 144) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 1728 a prime number?
No. 1728 = × , so it is divisible by 2.
What are the factors of 1728?
1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 27, 32, 36, 48, 54, 64, 72, 96, 108, 144, 192, 216, 288, 432, 576, 864, 1728.
What is 1728 in binary?
11011000000 (hexadecimal 6C0, octal 3300).
What is the square root of 1728?
About 41.5692, exactly 24√3.
What is 1728 in Roman numerals?
MDCCXXVIII.
Is 1728 divisible by 3?
Yes. Its digits add up to 18, a multiple of 3.
What is special about the number 1728?
1728 is a perfect cube (); a Harshad number: divisible by its digit sum 18.