The number 90200
90200 is a composite number with 48 divisors. Its prime factorisation is × × 11 × 41. Divisors (48): 1, 2, 4, 5, 8, 10, 11, 20, 22, 25, 40, 41, 44, 50, 55, 82 … 90200.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 90200: a Harshad number: divisible by its digit sum 11.
- 2
90200 is composite. Its prime factorisation is
- 3
The divisors add up to 234360; without 90200 itself that is 144160, so 90200 is abundant (144160 is more than 90200). Euler's totient φ(90200) = 32000 numbers up to 90200 share no factor with it.
- 4
The digits of 90200 add up to 11, and repeating that until one digit is left gives the digital root 2. The Collatz sequence (halve if even, else 3n+1) takes 89 steps to reach 1.
LaTeX source of the formulas on this page
\[ 90200 = 2^{3} \times 5^{2} \times 11 \times 41 \]90200 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 48 |
| Sum of divisors | 234360 |
| Euler totient φ(n) | 32000 |
| Square | 8136040000 |
| Cube | 733870808000000 |
| Square root | 300.333148 (= 10√902) |
| Digit sum / digital root | 11 / 2 |
| Collatz steps to 1 | 89 |
| Scientific notation | 9.02 × |
90200 in other forms
| Form | Value |
|---|---|
| In words | ninety thousand two hundred |
| Binary (base 2) | 10110000001011000 |
| Octal (base 8) | 260130 |
| Hexadecimal (base 16) | 16058 |
| Base 3 | 11120201202 |
| As time | 90200 seconds = 25 h 3 min 20 s |
Is 90200 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (90200 ÷ 2 = 45100) | 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 (90200 ÷ 4 = 22550) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | Yes (90200 ÷ 5 = 18040) | 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 5) | 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 (90200 ÷ 8 = 11275) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 2) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | Yes (90200 ÷ 10 = 9020) | A number is divisible by 10 if the last digit is 0. |
| 11 | Yes (90200 ÷ 11 = 8200) | 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 90200 a prime number?
No. 90200 = × × 11 × 41, so it is divisible by 2.
What are the factors of 90200?
1, 2, 4, 5, 8, 10, 11, 20, 22, 25, 40, 41, 44, 50, 55, 82, 88, 100, 110, 164, 200, 205, 220, 275, 328, 410, 440, 451, 550, 820, 902, 1025, 1100, 1640, 1804, 2050, 2200, 2255, 3608, 4100, 4510, 8200, 9020, 11275, 18040, 22550, 45100, 90200.
What is 90200 in binary?
10110000001011000 (hexadecimal 16058, octal 260130).
What is the square root of 90200?
About 300.3331, exactly 10√902.
Is 90200 divisible by 3?
No. Its digits add up to 11, which is not a multiple of 3.
What is special about the number 90200?
90200 is a Harshad number: divisible by its digit sum 11.