The number 90101
90101 is a binary palindrome (10101111111110101). Its prime factorisation is 11 × 8191. Divisors (4): 1, 11, 8191, 90101.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 90101: a binary palindrome (10101111111110101); a Harshad number: divisible by its digit sum 11; a semiprime: 11 × 8191, the product of two primes.
- 2
90101 is composite. Its prime factorisation is
- 3
The divisors add up to 98304; without 90101 itself that is 8203, so 90101 is deficient (8203 is less than 90101). Euler's totient φ(90101) = 81900 numbers up to 90101 share no factor with it.
- 4
The digits of 90101 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 164 steps to reach 1.
LaTeX source of the formulas on this page
\[ 90101 = 11 \times 8191 \]
90101 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 4 |
| Sum of divisors | 98304 |
| Euler totient φ(n) | 81900 |
| Square | 8118190201 |
| Cube | 731457055300301 |
| Square root | 300.168286 |
| Digit sum / digital root | 11 / 2 |
| Collatz steps to 1 | 164 |
| Scientific notation | 9.0101 × |
90101 in other forms
| Form | Value |
|---|---|
| In words | ninety thousand one hundred and one |
| Binary (base 2) | 10101111111110101 |
| Octal (base 8) | 257765 |
| Hexadecimal (base 16) | 15FF5 |
| Base 3 | 11120121002 |
| As time | 90101 seconds = 25 h 1 min 41 s |
Is 90101 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | No (remainder 1) | 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 | No (remainder 1) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | No (remainder 1) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | No (remainder 5) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 4) | 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 5) | 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 | No (remainder 1) | A number is divisible by 10 if the last digit is 0. |
| 11 | Yes (90101 ÷ 11 = 8191) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | No (remainder 5) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 90101 a prime number?
No. 90101 = 11 × 8191, so it is divisible by 11.
What are the factors of 90101?
1, 11, 8191, 90101.
What is 90101 in binary?
10101111111110101 (hexadecimal 15FF5, octal 257765).
What is the square root of 90101?
About 300.1683.
Is 90101 divisible by 3?
No. Its digits add up to 11, which is not a multiple of 3.
What is special about the number 90101?
90101 is a binary palindrome (10101111111110101); a Harshad number: divisible by its digit sum 11; a semiprime: 11 × 8191, the product of two primes.