The number 9993
9993 is a composite number with 4 divisors. Its prime factorisation is 3 × 3331. Divisors (4): 1, 3, 3331, 9993.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 9993: a semiprime: 3 × 3331, the product of two primes.
- 2
9993 is composite. Its prime factorisation is
- 3
The divisors add up to 13328; without 9993 itself that is 3335, so 9993 is deficient (3335 is less than 9993). Euler's totient φ(9993) = 6660 numbers up to 9993 share no factor with it.
- 4
The digits of 9993 add up to 30, and repeating that until one digit is left gives the digital root 3. The Collatz sequence (halve if even, else 3n+1) takes 73 steps to reach 1.
LaTeX source of the formulas on this page
\[ 9993 = 3 \times 3331 \]
9993 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 4 |
| Sum of divisors | 13328 |
| Euler totient φ(n) | 6660 |
| Square | 99860049 |
| Cube | 997901469657 |
| Square root | 99.964994 |
| Digit sum / digital root | 30 / 3 |
| Collatz steps to 1 | 73 |
| Scientific notation | 9.993 × |
9993 in other forms
| Form | Value |
|---|---|
| In words | nine thousand nine hundred and ninety-three |
| Binary (base 2) | 10011100001001 |
| Octal (base 8) | 23411 |
| Hexadecimal (base 16) | 2709 |
| Base 3 | 111201010 |
| As time | 9993 seconds = 2 h 46 min 33 s |
Is 9993 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 | Yes (9993 ÷ 3 = 3331) | 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 3) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | No (remainder 3) | 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 1) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 3) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | No (remainder 3) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 5) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | No (remainder 9) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 9993 a prime number?
No. 9993 = 3 × 3331, so it is divisible by 3.
What are the factors of 9993?
1, 3, 3331, 9993.
What is 9993 in binary?
10011100001001 (hexadecimal 2709, octal 23411).
What is the square root of 9993?
About 99.9650.
Is 9993 divisible by 3?
Yes. Its digits add up to 30, a multiple of 3.
What is special about the number 9993?
9993 is a semiprime: 3 × 3331, the product of two primes.