The number 88800
88800 is a composite number with 72 divisors. Its prime factorisation is × 3 × × 37. Divisors (72): 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 25, 30, 32 … 88800.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 88800: a happy number: repeatedly adding the squares of its digits reaches 1; a Harshad number: divisible by its digit sum 24.
- 2
88800 is composite. Its prime factorisation is
- 3
The divisors add up to 296856; without 88800 itself that is 208056, so 88800 is abundant (208056 is more than 88800). Euler's totient φ(88800) = 23040 numbers up to 88800 share no factor with it.
- 4
The digits of 88800 add up to 24, and repeating that until one digit is left gives the digital root 6. The Collatz sequence (halve if even, else 3n+1) takes 71 steps to reach 1.
LaTeX source of the formulas on this page
\[ 88800 = 2^{5} \times 3 \times 5^{2} \times 37 \]88800 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 72 |
| Sum of divisors | 296856 |
| Euler totient φ(n) | 23040 |
| Square | 7885440000 |
| Cube | 700227072000000 |
| Square root | 297.993289 (= 20√222) |
| Digit sum / digital root | 24 / 6 |
| Collatz steps to 1 | 71 |
| Scientific notation | 8.88 × |
88800 in other forms
| Form | Value |
|---|---|
| In words | eighty-eight thousand eight hundred |
| Binary (base 2) | 10101101011100000 |
| Octal (base 8) | 255340 |
| Hexadecimal (base 16) | 15AE0 |
| Base 3 | 11111210220 |
| As time | 88800 seconds = 24 h 40 min 0 s |
Is 88800 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (88800 ÷ 2 = 44400) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (88800 ÷ 3 = 29600) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (88800 ÷ 4 = 22200) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | Yes (88800 ÷ 5 = 17760) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (88800 ÷ 6 = 14800) | 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 (88800 ÷ 8 = 11100) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 6) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | Yes (88800 ÷ 10 = 8880) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 8) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (88800 ÷ 12 = 7400) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 88800 a prime number?
No. 88800 = × 3 × × 37, so it is divisible by 2.
What are the factors of 88800?
1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 25, 30, 32, 37, 40, 48, 50, 60, 74, 75, 80, 96, 100, 111, 120, 148, 150, 160, 185, 200, 222, 240, 296, 300, 370, 400, 444, 480, 555, 592, 600, 740, 800, 888, 925, 1110, 1184, 1200, 1480, 1776, 1850, 2220, 2400, 2775, 2960, 3552, 3700, 4440, 5550, 5920, 7400, 8880, 11100, 14800, 17760, 22200, 29600, 44400, 88800.
What is 88800 in binary?
10101101011100000 (hexadecimal 15AE0, octal 255340).
What is the square root of 88800?
About 297.9933, exactly 20√222.
Is 88800 divisible by 3?
Yes. Its digits add up to 24, a multiple of 3.
What is special about the number 88800?
88800 is a happy number: repeatedly adding the squares of its digits reaches 1; a Harshad number: divisible by its digit sum 24.