The number 9991
9991 is a composite number with 4 divisors. Its prime factorisation is 97 × 103. Divisors (4): 1, 97, 103, 9991.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 9991: a semiprime: 97 × 103, the product of two primes.
- 2
9991 is composite. Its prime factorisation is
- 3
The divisors add up to 10192; without 9991 itself that is 201, so 9991 is deficient (201 is less than 9991). Euler's totient φ(9991) = 9792 numbers up to 9991 share no factor with it.
- 4
The digits of 9991 add up to 28, and repeating that until one digit is left gives the digital root 1. The Collatz sequence (halve if even, else 3n+1) takes 166 steps to reach 1.
LaTeX source of the formulas on this page
\[ 9991 = 97 \times 103 \]
9991 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 4 |
| Sum of divisors | 10192 |
| Euler totient φ(n) | 9792 |
| Square | 99820081 |
| Cube | 997302429271 |
| Square root | 99.954990 |
| Digit sum / digital root | 28 / 1 |
| Collatz steps to 1 | 166 |
| Scientific notation | 9.991 × |
9991 in other forms
| Form | Value |
|---|---|
| In words | nine thousand nine hundred and ninety-one |
| Binary (base 2) | 10011100000111 |
| Octal (base 8) | 23407 |
| Hexadecimal (base 16) | 2707 |
| Base 3 | 111201001 |
| As time | 9991 seconds = 2 h 46 min 31 s |
Is 9991 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 3) | 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 2) | 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 7) | 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 3) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | No (remainder 7) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 9991 a prime number?
No. 9991 = 97 × 103, so it is divisible by 97.
What are the factors of 9991?
1, 97, 103, 9991.
What is 9991 in binary?
10011100000111 (hexadecimal 2707, octal 23407).
What is the square root of 9991?
About 99.9550.
Is 9991 divisible by 3?
No. Its digits add up to 28, which is not a multiple of 3.
What is special about the number 9991?
9991 is a semiprime: 97 × 103, the product of two primes.