The number 10188
10188 is a composite number with 18 divisors. Its prime factorisation is × × 283. Divisors (18): 1, 2, 3, 4, 6, 9, 12, 18, 36, 283, 566, 849, 1132, 1698, 2547, 3396 … 10188.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 10188: a happy number: repeatedly adding the squares of its digits reaches 1; a Harshad number: divisible by its digit sum 18.
- 2
10188 is composite. Its prime factorisation is
- 3
The divisors add up to 25844; without 10188 itself that is 15656, so 10188 is abundant (15656 is more than 10188). Euler's totient φ(10188) = 3384 numbers up to 10188 share no factor with it.
- 4
The digits of 10188 add up to 18, and repeating that until one digit is left gives the digital root 9. The Collatz sequence (halve if even, else 3n+1) takes 34 steps to reach 1.
LaTeX source of the formulas on this page
\[ 10188 = 2^{2} \times 3^{2} \times 283 \]10188 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 18 |
| Sum of divisors | 25844 |
| Euler totient φ(n) | 3384 |
| Square | 103795344 |
| Cube | 1057466964672 |
| Square root | 100.935623 (= 6√283) |
| Digit sum / digital root | 18 / 9 |
| Collatz steps to 1 | 34 |
| Scientific notation | 1.0188 × |
10188 in other forms
| Form | Value |
|---|---|
| In words | ten thousand one hundred and eighty-eight |
| Binary (base 2) | 10011111001100 |
| Octal (base 8) | 23714 |
| Hexadecimal (base 16) | 27CC |
| Base 3 | 111222100 |
| As time | 10188 seconds = 2 h 49 min 48 s |
Is 10188 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (10188 ÷ 2 = 5094) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (10188 ÷ 3 = 3396) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (10188 ÷ 4 = 2547) | 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 (10188 ÷ 6 = 1698) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 3) | 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 | No (remainder 4) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | Yes (10188 ÷ 9 = 1132) | 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 2) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (10188 ÷ 12 = 849) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 10188 a prime number?
No. 10188 = × × 283, so it is divisible by 2.
What are the factors of 10188?
1, 2, 3, 4, 6, 9, 12, 18, 36, 283, 566, 849, 1132, 1698, 2547, 3396, 5094, 10188.
What is 10188 in binary?
10011111001100 (hexadecimal 27CC, octal 23714).
What is the square root of 10188?
About 100.9356, exactly 6√283.
Is 10188 divisible by 3?
Yes. Its digits add up to 18, a multiple of 3.
What is special about the number 10188?
10188 is a happy number: repeatedly adding the squares of its digits reaches 1; a Harshad number: divisible by its digit sum 18.