The number 88080
88080 is a composite number with 40 divisors. Its prime factorisation is × 3 × 5 × 367. Divisors (40): 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 40, 48 … 88080.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 88080: a happy number: repeatedly adding the squares of its digits reaches 1; a Harshad number: divisible by its digit sum 24.
- 2
88080 is composite. Its prime factorisation is
- 3
The divisors add up to 273792; without 88080 itself that is 185712, so 88080 is abundant (185712 is more than 88080). Euler's totient φ(88080) = 23424 numbers up to 88080 share no factor with it.
- 4
The digits of 88080 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 195 steps to reach 1.
LaTeX source of the formulas on this page
\[ 88080 = 2^{4} \times 3 \times 5 \times 367 \]88080 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 40 |
| Sum of divisors | 273792 |
| Euler totient φ(n) | 23424 |
| Square | 7758086400 |
| Cube | 683332250112000 |
| Square root | 296.782749 (= 4√5505) |
| Digit sum / digital root | 24 / 6 |
| Collatz steps to 1 | 195 |
| Scientific notation | 8.808 × |
88080 in other forms
| Form | Value |
|---|---|
| In words | eighty-eight thousand and eighty |
| Binary (base 2) | 10101100000010000 |
| Octal (base 8) | 254020 |
| Hexadecimal (base 16) | 15810 |
| Base 3 | 11110211020 |
| As time | 88080 seconds = 24 h 28 min 0 s |
Is 88080 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (88080 ÷ 2 = 44040) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (88080 ÷ 3 = 29360) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (88080 ÷ 4 = 22020) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | Yes (88080 ÷ 5 = 17616) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (88080 ÷ 6 = 14680) | 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 (88080 ÷ 8 = 11010) | 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 (88080 ÷ 10 = 8808) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 3) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (88080 ÷ 12 = 7340) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 88080 a prime number?
No. 88080 = × 3 × 5 × 367, so it is divisible by 2.
What are the factors of 88080?
1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 40, 48, 60, 80, 120, 240, 367, 734, 1101, 1468, 1835, 2202, 2936, 3670, 4404, 5505, 5872, 7340, 8808, 11010, 14680, 17616, 22020, 29360, 44040, 88080.
What is 88080 in binary?
10101100000010000 (hexadecimal 15810, octal 254020).
What is the square root of 88080?
About 296.7827, exactly 4√5505.
Is 88080 divisible by 3?
Yes. Its digits add up to 24, a multiple of 3.
What is special about the number 88080?
88080 is a happy number: repeatedly adding the squares of its digits reaches 1; a Harshad number: divisible by its digit sum 24.