The number 90112
90112 is a composite number with 28 divisors. Its prime factorisation is × 11. Divisors (28): 1, 2, 4, 8, 11, 16, 22, 32, 44, 64, 88, 128, 176, 256, 352, 512 … 90112.
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How to work it out
- 1
90112 has no famous special property in the usual lists (prime, square, cube, triangular, Fibonacci, palindrome, perfect), but it is still a composite number.
- 2
90112 is composite. Its prime factorisation is
- 3
The divisors add up to 196596; without 90112 itself that is 106484, so 90112 is abundant (106484 is more than 90112). Euler's totient φ(90112) = 40960 numbers up to 90112 share no factor with it.
- 4
The digits of 90112 add up to 13, and repeating that until one digit is left gives the digital root 4. The Collatz sequence (halve if even, else 3n+1) takes 27 steps to reach 1.
LaTeX source of the formulas on this page
\[ 90112 = 2^{13} \times 11 \]90112 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 28 |
| Sum of divisors | 196596 |
| Euler totient φ(n) | 40960 |
| Square | 8120172544 |
| Cube | 731724988284928 |
| Square root | 300.186609 (= 64√22) |
| Digit sum / digital root | 13 / 4 |
| Collatz steps to 1 | 27 |
| Scientific notation | 9.0112 × |
90112 in other forms
| Form | Value |
|---|---|
| In words | ninety thousand one hundred and twelve |
| Binary (base 2) | 10110000000000000 |
| Octal (base 8) | 260000 |
| Hexadecimal (base 16) | 16000 |
| Base 3 | 11120121111 |
| As time | 90112 seconds = 25 h 1 min 52 s |
Is 90112 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (90112 ÷ 2 = 45056) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | No (remainder 1) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (90112 ÷ 4 = 22528) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | No (remainder 2) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | No (remainder 4) | 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 (90112 ÷ 8 = 11264) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 4) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | No (remainder 2) | A number is divisible by 10 if the last digit is 0. |
| 11 | Yes (90112 ÷ 11 = 8192) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | No (remainder 4) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 90112 a prime number?
No. 90112 = × 11, so it is divisible by 2.
What are the factors of 90112?
1, 2, 4, 8, 11, 16, 22, 32, 44, 64, 88, 128, 176, 256, 352, 512, 704, 1024, 1408, 2048, 2816, 4096, 5632, 8192, 11264, 22528, 45056, 90112.
What is 90112 in binary?
10110000000000000 (hexadecimal 16000, octal 260000).
What is the square root of 90112?
About 300.1866, exactly 64√22.
Is 90112 divisible by 3?
No. Its digits add up to 13, which is not a multiple of 3.
What is special about the number 90112?
It is a composite number with 28 divisors.