The number 1791
1791 is a composite number with 6 divisors. Its prime factorisation is × 199. Divisors (6): 1, 3, 9, 199, 597, 1791.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
1791 has no famous special property in the usual lists (prime, square, cube, triangular, Fibonacci, palindrome, perfect), but it is still a composite number.
- 2
1791 is composite. Its prime factorisation is
- 3
The divisors add up to 2600; without 1791 itself that is 809, so 1791 is deficient (809 is less than 1791). Euler's totient φ(1791) = 1188 numbers up to 1791 share no factor with it.
- 4
The digits of 1791 add up to 18, and repeating that until one digit is left gives the digital root 9. The Collatz sequence (halve if even, else 3n+1) takes 99 steps to reach 1.
LaTeX source of the formulas on this page
\[ 1791 = 3^{2} \times 199 \]1791 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 6 |
| Sum of divisors | 2600 |
| Euler totient φ(n) | 1188 |
| Square | 3207681 |
| Cube | 5744956671 |
| Square root | 42.320208 (= 3√199) |
| Digit sum / digital root | 18 / 9 |
| Collatz steps to 1 | 99 |
| Scientific notation | 1.791 × |
1791 in other forms
| Form | Value |
|---|---|
| In words | one thousand seven hundred and ninety-one |
| Roman numerals | MDCCXCI |
| Binary (base 2) | 11011111111 |
| Octal (base 8) | 3377 |
| Hexadecimal (base 16) | 6FF |
| Base 3 | 2110100 |
| As time | 1791 seconds = 29 min 51 s |
Is 1791 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 (1791 ÷ 3 = 597) | 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 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 7) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | Yes (1791 ÷ 9 = 199) | 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 9) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | No (remainder 3) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 1791 a prime number?
No. 1791 = × 199, so it is divisible by 3.
What are the factors of 1791?
1, 3, 9, 199, 597, 1791.
What is 1791 in binary?
11011111111 (hexadecimal 6FF, octal 3377).
What is the square root of 1791?
About 42.3202, exactly 3√199.
What is 1791 in Roman numerals?
MDCCXCI.
Is 1791 divisible by 3?
Yes. Its digits add up to 18, a multiple of 3.
What is special about the number 1791?
It is a composite number with 6 divisors.