The number 90090
90090 is a composite number with 96 divisors. Its prime factorisation is 2 × × 5 × 7 × 11 × 13. Divisors (96): 1, 2, 3, 5, 6, 7, 9, 10, 11, 13, 14, 15, 18, 21, 22, 26 … 90090.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 90090: a Harshad number: divisible by its digit sum 18.
- 2
90090 is composite. Its prime factorisation is
- 3
The divisors add up to 314496; without 90090 itself that is 224406, so 90090 is abundant (224406 is more than 90090). Euler's totient φ(90090) = 17280 numbers up to 90090 share no factor with it.
- 4
The digits of 90090 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 164 steps to reach 1.
LaTeX source of the formulas on this page
\[ 90090 = 2 \times 3^{2} \times 5 \times 7 \times 11 \times 13 \]90090 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 96 |
| Sum of divisors | 314496 |
| Euler totient φ(n) | 17280 |
| Square | 8116208100 |
| Cube | 731189187729000 |
| Square root | 300.149963 (= 3√10010) |
| Digit sum / digital root | 18 / 9 |
| Collatz steps to 1 | 164 |
| Scientific notation | 9.009 × |
90090 in other forms
| Form | Value |
|---|---|
| In words | ninety thousand and ninety |
| Binary (base 2) | 10101111111101010 |
| Octal (base 8) | 257752 |
| Hexadecimal (base 16) | 15FEA |
| Base 3 | 11120120200 |
| As time | 90090 seconds = 25 h 1 min 30 s |
Is 90090 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (90090 ÷ 2 = 45045) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (90090 ÷ 3 = 30030) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | No (remainder 2) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | Yes (90090 ÷ 5 = 18018) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (90090 ÷ 6 = 15015) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | Yes (90090 ÷ 7 = 12870) | 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 2) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | Yes (90090 ÷ 9 = 10010) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | Yes (90090 ÷ 10 = 9009) | A number is divisible by 10 if the last digit is 0. |
| 11 | Yes (90090 ÷ 11 = 8190) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | No (remainder 6) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 90090 a prime number?
No. 90090 = 2 × × 5 × 7 × 11 × 13, so it is divisible by 2.
What are the factors of 90090?
1, 2, 3, 5, 6, 7, 9, 10, 11, 13, 14, 15, 18, 21, 22, 26, 30, 33, 35, 39, 42, 45, 55, 63, 65, 66, 70, 77, 78, 90, 91, 99, 105, 110, 117, 126, 130, 143, 154, 165, 182, 195, 198, 210, 231, 234, 273, 286, 315, 330, 385, 390, 429, 455, 462, 495, 546, 585, 630, 693, 715, 770, 819, 858, 910, 990, 1001, 1155, 1170, 1287, 1365, 1386, 1430, 1638, 2002, 2145, 2310, 2574, 2730, 3003, 3465, 4095, 4290, 5005, 6006, 6435, 6930, 8190, 9009, 10010, 12870, 15015, 18018, 30030, 45045, 90090.
What is 90090 in binary?
10101111111101010 (hexadecimal 15FEA, octal 257752).
What is the square root of 90090?
About 300.1500, exactly 3√10010.
Is 90090 divisible by 3?
Yes. Its digits add up to 18, a multiple of 3.
What is special about the number 90090?
90090 is a Harshad number: divisible by its digit sum 18.