The number 993
993 is a composite number with 4 divisors. Its prime factorisation is 3 × 331. Divisors (4): 1, 3, 331, 993.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 993: a semiprime: 3 × 331, the product of two primes.
- 2
993 is composite. Its prime factorisation is
- 3
The divisors add up to 1328; without 993 itself that is 335, so 993 is deficient (335 is less than 993). Euler's totient φ(993) = 660 numbers up to 993 share no factor with it.
- 4
The digits of 993 add up to 21, and repeating that until one digit is left gives the digital root 3. The Collatz sequence (halve if even, else 3n+1) takes 93 steps to reach 1.
LaTeX source of the formulas on this page
\[ 993 = 3 \times 331 \]
993 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 4 |
| Sum of divisors | 1328 |
| Euler totient φ(n) | 660 |
| Square | 986049 |
| Cube | 979146657 |
| Square root | 31.511903 |
| Digit sum / digital root | 21 / 3 |
| Collatz steps to 1 | 93 |
| Scientific notation | 9.93 × |
993 in other forms
| Form | Value |
|---|---|
| In words | nine hundred and ninety-three |
| Roman numerals | CMXCIII |
| Binary (base 2) | 1111100001 |
| Octal (base 8) | 1741 |
| Hexadecimal (base 16) | 3E1 |
| Base 3 | 1100210 |
| As time | 993 seconds = 16 min 33 s |
Is 993 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 (993 ÷ 3 = 331) | 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 6) | 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 3) | 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 993 a prime number?
No. 993 = 3 × 331, so it is divisible by 3.
What are the factors of 993?
1, 3, 331, 993.
What is 993 in binary?
1111100001 (hexadecimal 3E1, octal 1741).
What is the square root of 993?
About 31.5119.
What is 993 in Roman numerals?
CMXCIII.
Is 993 divisible by 3?
Yes. Its digits add up to 21, a multiple of 3.
What is special about the number 993?
993 is a semiprime: 3 × 331, the product of two primes.