The number 10088
10088 is a composite number with 16 divisors. Its prime factorisation is × 13 × 97. Divisors (16): 1, 2, 4, 8, 13, 26, 52, 97, 104, 194, 388, 776, 1261, 2522, 5044, 10088.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 10088: a happy number: repeatedly adding the squares of its digits reaches 1.
- 2
10088 is composite. Its prime factorisation is
- 3
The divisors add up to 20580; without 10088 itself that is 10492, so 10088 is abundant (10492 is more than 10088). Euler's totient φ(10088) = 4608 numbers up to 10088 share no factor with it.
- 4
The digits of 10088 add up to 17, and repeating that until one digit is left gives the digital root 8. The Collatz sequence (halve if even, else 3n+1) takes 42 steps to reach 1.
LaTeX source of the formulas on this page
\[ 10088 = 2^{3} \times 13 \times 97 \]10088 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 16 |
| Sum of divisors | 20580 |
| Euler totient φ(n) | 4608 |
| Square | 101767744 |
| Cube | 1026633001472 |
| Square root | 100.439036 (= 2√2522) |
| Digit sum / digital root | 17 / 8 |
| Collatz steps to 1 | 42 |
| Scientific notation | 1.0088 × |
10088 in other forms
| Form | Value |
|---|---|
| In words | ten thousand and eighty-eight |
| Binary (base 2) | 10011101101000 |
| Octal (base 8) | 23550 |
| Hexadecimal (base 16) | 2768 |
| Base 3 | 111211122 |
| As time | 10088 seconds = 2 h 48 min 8 s |
Is 10088 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (10088 ÷ 2 = 5044) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | No (remainder 2) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (10088 ÷ 4 = 2522) | 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 | No (remainder 2) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 1) | 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 (10088 ÷ 8 = 1261) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 8) | 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 1) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | No (remainder 8) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 10088 a prime number?
No. 10088 = × 13 × 97, so it is divisible by 2.
What are the factors of 10088?
1, 2, 4, 8, 13, 26, 52, 97, 104, 194, 388, 776, 1261, 2522, 5044, 10088.
What is 10088 in binary?
10011101101000 (hexadecimal 2768, octal 23550).
What is the square root of 10088?
About 100.4390, exactly 2√2522.
Is 10088 divisible by 3?
No. Its digits add up to 17, which is not a multiple of 3.
What is special about the number 10088?
10088 is a happy number: repeatedly adding the squares of its digits reaches 1.