The number 88032
88032 is a composite number with 48 divisors. Its prime factorisation is × 3 × 7 × 131. Divisors (48): 1, 2, 3, 4, 6, 7, 8, 12, 14, 16, 21, 24, 28, 32, 42, 48 … 88032.
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How to work it out
- 1
What is special about 88032: a Harshad number: divisible by its digit sum 21.
- 2
88032 is composite. Its prime factorisation is
- 3
The divisors add up to 266112; without 88032 itself that is 178080, so 88032 is abundant (178080 is more than 88032). Euler's totient φ(88032) = 24960 numbers up to 88032 share no factor with it.
- 4
The digits of 88032 add up to 21, and repeating that until one digit is left gives the digital root 3. The Collatz sequence (halve if even, else 3n+1) takes 177 steps to reach 1.
LaTeX source of the formulas on this page
\[ 88032 = 2^{5} \times 3 \times 7 \times 131 \]88032 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 48 |
| Sum of divisors | 266112 |
| Euler totient φ(n) | 24960 |
| Square | 7749633024 |
| Cube | 682215694368768 |
| Square root | 296.701871 (= 4√5502) |
| Digit sum / digital root | 21 / 3 |
| Collatz steps to 1 | 177 |
| Scientific notation | 8.8032 × |
88032 in other forms
| Form | Value |
|---|---|
| In words | eighty-eight thousand and thirty-two |
| Binary (base 2) | 10101011111100000 |
| Octal (base 8) | 253740 |
| Hexadecimal (base 16) | 157E0 |
| Base 3 | 11110202110 |
| As time | 88032 seconds = 24 h 27 min 12 s |
Is 88032 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (88032 ÷ 2 = 44016) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (88032 ÷ 3 = 29344) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (88032 ÷ 4 = 22008) | 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 (88032 ÷ 6 = 14672) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | Yes (88032 ÷ 7 = 12576) | 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 (88032 ÷ 8 = 11004) | 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 2) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 10) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (88032 ÷ 12 = 7336) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 88032 a prime number?
No. 88032 = × 3 × 7 × 131, so it is divisible by 2.
What are the factors of 88032?
1, 2, 3, 4, 6, 7, 8, 12, 14, 16, 21, 24, 28, 32, 42, 48, 56, 84, 96, 112, 131, 168, 224, 262, 336, 393, 524, 672, 786, 917, 1048, 1572, 1834, 2096, 2751, 3144, 3668, 4192, 5502, 6288, 7336, 11004, 12576, 14672, 22008, 29344, 44016, 88032.
What is 88032 in binary?
10101011111100000 (hexadecimal 157E0, octal 253740).
What is the square root of 88032?
About 296.7019, exactly 4√5502.
Is 88032 divisible by 3?
Yes. Its digits add up to 21, a multiple of 3.
What is special about the number 88032?
88032 is a Harshad number: divisible by its digit sum 21.