The number 88008
88008 is a composite number with 32 divisors. Its prime factorisation is × 3 × 19 × 193. Divisors (32): 1, 2, 3, 4, 6, 8, 12, 19, 24, 38, 57, 76, 114, 152, 193, 228 … 88008.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 88008: a happy number: repeatedly adding the squares of its digits reaches 1; a Harshad number: divisible by its digit sum 24.
- 2
88008 is composite. Its prime factorisation is
- 3
The divisors add up to 232800; without 88008 itself that is 144792, so 88008 is abundant (144792 is more than 88008). Euler's totient φ(88008) = 27648 numbers up to 88008 share no factor with it.
- 4
The digits of 88008 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
\[ 88008 = 2^{3} \times 3 \times 19 \times 193 \]88008 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 32 |
| Sum of divisors | 232800 |
| Euler totient φ(n) | 27648 |
| Square | 7745408064 |
| Cube | 681657872896512 |
| Square root | 296.661423 (= 2√22002) |
| Digit sum / digital root | 24 / 6 |
| Collatz steps to 1 | 71 |
| Scientific notation | 8.8008 × |
88008 in other forms
| Form | Value |
|---|---|
| In words | eighty-eight thousand and eight |
| Binary (base 2) | 10101011111001000 |
| Octal (base 8) | 253710 |
| Hexadecimal (base 16) | 157C8 |
| Base 3 | 11110201120 |
| As time | 88008 seconds = 24 h 26 min 48 s |
Is 88008 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (88008 ÷ 2 = 44004) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (88008 ÷ 3 = 29336) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (88008 ÷ 4 = 22002) | 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 (88008 ÷ 6 = 14668) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 4) | 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 (88008 ÷ 8 = 11001) | 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 | No (remainder 8) | 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 (88008 ÷ 12 = 7334) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 88008 a prime number?
No. 88008 = × 3 × 19 × 193, so it is divisible by 2.
What are the factors of 88008?
1, 2, 3, 4, 6, 8, 12, 19, 24, 38, 57, 76, 114, 152, 193, 228, 386, 456, 579, 772, 1158, 1544, 2316, 3667, 4632, 7334, 11001, 14668, 22002, 29336, 44004, 88008.
What is 88008 in binary?
10101011111001000 (hexadecimal 157C8, octal 253710).
What is the square root of 88008?
About 296.6614, exactly 2√22002.
Is 88008 divisible by 3?
Yes. Its digits add up to 24, a multiple of 3.
What is special about the number 88008?
88008 is a happy number: repeatedly adding the squares of its digits reaches 1; a Harshad number: divisible by its digit sum 24.