The number 67728
67728 is a composite number with 40 divisors. Its prime factorisation is × 3 × 17 × 83. Divisors (40): 1, 2, 3, 4, 6, 8, 12, 16, 17, 24, 34, 48, 51, 68, 83, 102 … 67728.
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How to work it out
- 1
67728 has no famous special property in the usual lists (prime, square, cube, triangular, Fibonacci, palindrome, perfect), but it is still a composite number.
- 2
67728 is composite. Its prime factorisation is
- 3
The divisors add up to 187488; without 67728 itself that is 119760, so 67728 is abundant (119760 is more than 67728). Euler's totient φ(67728) = 20992 numbers up to 67728 share no factor with it.
- 4
The digits of 67728 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 205 steps to reach 1.
LaTeX source of the formulas on this page
\[ 67728 = 2^{4} \times 3 \times 17 \times 83 \]67728 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 40 |
| Sum of divisors | 187488 |
| Euler totient φ(n) | 20992 |
| Square | 4587081984 |
| Cube | 310673888612352 |
| Square root | 260.246037 (= 4√4233) |
| Digit sum / digital root | 30 / 3 |
| Collatz steps to 1 | 205 |
| Scientific notation | 6.7728 × |
67728 in other forms
| Form | Value |
|---|---|
| In words | sixty-seven thousand seven hundred and twenty-eight |
| Binary (base 2) | 10000100010010000 |
| Octal (base 8) | 204220 |
| Hexadecimal (base 16) | 10890 |
| Base 3 | 10102220110 |
| As time | 67728 seconds = 18 h 48 min 48 s |
Is 67728 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (67728 ÷ 2 = 33864) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (67728 ÷ 3 = 22576) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (67728 ÷ 4 = 16932) | 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 (67728 ÷ 6 = 11288) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 3) | 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 (67728 ÷ 8 = 8466) | 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 1) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (67728 ÷ 12 = 5644) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 67728 a prime number?
No. 67728 = × 3 × 17 × 83, so it is divisible by 2.
What are the factors of 67728?
1, 2, 3, 4, 6, 8, 12, 16, 17, 24, 34, 48, 51, 68, 83, 102, 136, 166, 204, 249, 272, 332, 408, 498, 664, 816, 996, 1328, 1411, 1992, 2822, 3984, 4233, 5644, 8466, 11288, 16932, 22576, 33864, 67728.
What is 67728 in binary?
10000100010010000 (hexadecimal 10890, octal 204220).
What is the square root of 67728?
About 260.2460, exactly 4√4233.
Is 67728 divisible by 3?
Yes. Its digits add up to 30, a multiple of 3.
What is special about the number 67728?
It is a composite number with 40 divisors.