The number 1991
1991 is a palindrome: it reads 1991 backwards too. Its prime factorisation is 11 × 181. Divisors (4): 1, 11, 181, 1991.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 1991: a palindrome: it reads 1991 backwards too; a semiprime: 11 × 181, the product of two primes.
- 2
1991 is composite. Its prime factorisation is
- 3
The divisors add up to 2184; without 1991 itself that is 193, so 1991 is deficient (193 is less than 1991). Euler's totient φ(1991) = 1800 numbers up to 1991 share no factor with it.
- 4
The digits of 1991 add up to 20, and repeating that until one digit is left gives the digital root 2. The Collatz sequence (halve if even, else 3n+1) takes 50 steps to reach 1.
LaTeX source of the formulas on this page
\[ 1991 = 11 \times 181 \]
1991 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 4 |
| Sum of divisors | 2184 |
| Euler totient φ(n) | 1800 |
| Square | 3964081 |
| Cube | 7892485271 |
| Square root | 44.620623 |
| Digit sum / digital root | 20 / 2 |
| Collatz steps to 1 | 50 |
| Scientific notation | 1.991 × |
1991 in other forms
| Form | Value |
|---|---|
| In words | one thousand nine hundred and ninety-one |
| Roman numerals | MCMXCI |
| Binary (base 2) | 11111000111 |
| Octal (base 8) | 3707 |
| Hexadecimal (base 16) | 7C7 |
| Base 3 | 2201202 |
| As time | 1991 seconds = 33 min 11 s |
Is 1991 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 2) | 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 5) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 3) | 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 2) | 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 | Yes (1991 ÷ 11 = 181) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | No (remainder 11) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 1991 a prime number?
No. 1991 = 11 × 181, so it is divisible by 11.
What are the factors of 1991?
1, 11, 181, 1991.
What is 1991 in binary?
11111000111 (hexadecimal 7C7, octal 3707).
What is the square root of 1991?
About 44.6206.
What is 1991 in Roman numerals?
MCMXCI.
Is 1991 divisible by 3?
No. Its digits add up to 20, which is not a multiple of 3.
What is special about the number 1991?
1991 is a palindrome: it reads 1991 backwards too; a semiprime: 11 × 181, the product of two primes.