The number 9901
9901 is the 1221st prime number. Its only divisors are 1 and 9901.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 9901: the 1221st prime number.
- 2
9901 is prime, so its only factors are 1 and 9901. It is the 1221st prime; the next prime is 9907 and the one before is 9887.
- 3
The divisors add up to 9902; without 9901 itself that is 1, so 9901 is deficient (1 is less than 9901). Euler's totient φ(9901) = 9900 numbers up to 9901 share no factor with it.
- 4
The digits of 9901 add up to 19, and repeating that until one digit is left gives the digital root 1. The Collatz sequence (halve if even, else 3n+1) takes 73 steps to reach 1.
9901 at a glance
| Property | Value |
|---|---|
| Type | prime |
| Number of divisors | 2 |
| Sum of divisors | 9902 |
| Euler totient φ(n) | 9900 |
| Square | 98029801 |
| Cube | 970593059701 |
| Square root | 99.503769 |
| Digit sum / digital root | 19 / 1 |
| Collatz steps to 1 | 73 |
| Scientific notation | 9.901 × |
9901 in other forms
| Form | Value |
|---|---|
| In words | nine thousand nine hundred and one |
| Binary (base 2) | 10011010101101 |
| Octal (base 8) | 23255 |
| Hexadecimal (base 16) | 26AD |
| Base 3 | 111120201 |
| As time | 9901 seconds = 2 h 45 min 1 s |
Is 9901 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 1) | 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 1) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 3) | 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 1) | 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 | No (remainder 1) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | No (remainder 1) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 9901 a prime number?
Yes. 9901 is divisible only by 1 and itself.
What are the factors of 9901?
1, 9901.
What is 9901 in binary?
10011010101101 (hexadecimal 26AD, octal 23255).
What is the square root of 9901?
About 99.5038.
Is 9901 divisible by 3?
No. Its digits add up to 19, which is not a multiple of 3.
What is special about the number 9901?
9901 is the 1221st prime number.