The number 90084
90084 is a composite number with 12 divisors. Its prime factorisation is × 3 × 7507. Divisors (12): 1, 2, 3, 4, 6, 12, 7507, 15014, 22521, 30028, 45042, 90084.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
90084 has no famous special property in the usual lists (prime, square, cube, triangular, Fibonacci, palindrome, perfect), but it is still a composite number.
- 2
90084 is composite. Its prime factorisation is
- 3
The divisors add up to 210224; without 90084 itself that is 120140, so 90084 is abundant (120140 is more than 90084). Euler's totient φ(90084) = 30024 numbers up to 90084 share no factor with it.
- 4
The digits of 90084 add up to 21, and repeating that until one digit is left gives the digital root 3. The Collatz sequence (halve if even, else 3n+1) takes 164 steps to reach 1.
LaTeX source of the formulas on this page
\[ 90084 = 2^{2} \times 3 \times 7507 \]90084 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 12 |
| Sum of divisors | 210224 |
| Euler totient φ(n) | 30024 |
| Square | 8115127056 |
| Cube | 731043105712704 |
| Square root | 300.139967 (= 2√22521) |
| Digit sum / digital root | 21 / 3 |
| Collatz steps to 1 | 164 |
| Scientific notation | 9.0084 × |
90084 in other forms
| Form | Value |
|---|---|
| In words | ninety thousand and eighty-four |
| Binary (base 2) | 10101111111100100 |
| Octal (base 8) | 257744 |
| Hexadecimal (base 16) | 15FE4 |
| Base 3 | 11120120110 |
| As time | 90084 seconds = 25 h 1 min 24 s |
Is 90084 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (90084 ÷ 2 = 45042) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (90084 ÷ 3 = 30028) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (90084 ÷ 4 = 22521) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | No (remainder 4) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (90084 ÷ 6 = 15014) | 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 | No (remainder 4) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 3) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | No (remainder 4) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 5) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (90084 ÷ 12 = 7507) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 90084 a prime number?
No. 90084 = × 3 × 7507, so it is divisible by 2.
What are the factors of 90084?
1, 2, 3, 4, 6, 12, 7507, 15014, 22521, 30028, 45042, 90084.
What is 90084 in binary?
10101111111100100 (hexadecimal 15FE4, octal 257744).
What is the square root of 90084?
About 300.1400, exactly 2√22521.
Is 90084 divisible by 3?
Yes. Its digits add up to 21, a multiple of 3.
What is special about the number 90084?
It is a composite number with 12 divisors.