The number 1993
1993 is the 301st prime number. Its only divisors are 1 and 1993.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 1993: the 301st prime number.
- 2
1993 is prime, so its only factors are 1 and 1993. It is the 301st prime; the next prime is 1997 and the one before is 1987.
- 3
The divisors add up to 1994; without 1993 itself that is 1, so 1993 is deficient (1 is less than 1993). Euler's totient φ(1993) = 1992 numbers up to 1993 share no factor with it.
- 4
The digits of 1993 add up to 22, and repeating that until one digit is left gives the digital root 4. The Collatz sequence (halve if even, else 3n+1) takes 50 steps to reach 1.
1993 at a glance
| Property | Value |
|---|---|
| Type | prime |
| Number of divisors | 2 |
| Sum of divisors | 1994 |
| Euler totient φ(n) | 1992 |
| Square | 3972049 |
| Cube | 7916293657 |
| Square root | 44.643029 |
| Digit sum / digital root | 22 / 4 |
| Collatz steps to 1 | 50 |
| Scientific notation | 1.993 × |
1993 in other forms
| Form | Value |
|---|---|
| In words | one thousand nine hundred and ninety-three |
| Roman numerals | MCMXCIII |
| Binary (base 2) | 11111001001 |
| Octal (base 8) | 3711 |
| Hexadecimal (base 16) | 7C9 |
| Base 3 | 2201211 |
| As time | 1993 seconds = 33 min 13 s |
Is 1993 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 3) | 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 5) | 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 4) | 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 2) | 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 1993 a prime number?
Yes. 1993 is divisible only by 1 and itself.
What are the factors of 1993?
1, 1993.
What is 1993 in binary?
11111001001 (hexadecimal 7C9, octal 3711).
What is the square root of 1993?
About 44.6430.
What is 1993 in Roman numerals?
MCMXCIII.
Is 1993 divisible by 3?
No. Its digits add up to 22, which is not a multiple of 3.
What is special about the number 1993?
1993 is the 301st prime number.