The number 88128
88128 is a composite number with 70 divisors. Its prime factorisation is × × 17. Divisors (70): 1, 2, 3, 4, 6, 8, 9, 12, 16, 17, 18, 24, 27, 32, 34, 36 … 88128.
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How to work it out
- 1
What is special about 88128: a Harshad number: divisible by its digit sum 27.
- 2
88128 is composite. Its prime factorisation is
- 3
The divisors add up to 276606; without 88128 itself that is 188478, so 88128 is abundant (188478 is more than 88128). Euler's totient φ(88128) = 27648 numbers up to 88128 share no factor with it.
- 4
The digits of 88128 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 164 steps to reach 1.
LaTeX source of the formulas on this page
\[ 88128 = 2^{6} \times 3^{4} \times 17 \]88128 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 70 |
| Sum of divisors | 276606 |
| Euler totient φ(n) | 27648 |
| Square | 7766544384 |
| Cube | 684450023473152 |
| Square root | 296.863605 (= 72√17) |
| Digit sum / digital root | 27 / 9 |
| Collatz steps to 1 | 164 |
| Scientific notation | 8.8128 × |
88128 in other forms
| Form | Value |
|---|---|
| In words | eighty-eight thousand one hundred and twenty-eight |
| Binary (base 2) | 10101100001000000 |
| Octal (base 8) | 254100 |
| Hexadecimal (base 16) | 15840 |
| Base 3 | 11110220000 |
| As time | 88128 seconds = 24 h 28 min 48 s |
Is 88128 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (88128 ÷ 2 = 44064) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (88128 ÷ 3 = 29376) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (88128 ÷ 4 = 22032) | 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 (88128 ÷ 6 = 14688) | 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 | Yes (88128 ÷ 8 = 11016) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | Yes (88128 ÷ 9 = 9792) | 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 7) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (88128 ÷ 12 = 7344) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 88128 a prime number?
No. 88128 = × × 17, so it is divisible by 2.
What are the factors of 88128?
1, 2, 3, 4, 6, 8, 9, 12, 16, 17, 18, 24, 27, 32, 34, 36, 48, 51, 54, 64, 68, 72, 81, 96, 102, 108, 136, 144, 153, 162, 192, 204, 216, 272, 288, 306, 324, 408, 432, 459, 544, 576, 612, 648, 816, 864, 918, 1088, 1224, 1296, 1377, 1632, 1728, 1836, 2448, 2592, 2754, 3264, 3672, 4896, 5184, 5508, 7344, 9792, 11016, 14688, 22032, 29376, 44064, 88128.
What is 88128 in binary?
10101100001000000 (hexadecimal 15840, octal 254100).
What is the square root of 88128?
About 296.8636, exactly 72√17.
Is 88128 divisible by 3?
Yes. Its digits add up to 27, a multiple of 3.
What is special about the number 88128?
88128 is a Harshad number: divisible by its digit sum 27.