The number 1891
1891 is a triangular number: 1 + 2 + … + 61 = 1891. Its prime factorisation is 31 × 61. Divisors (4): 1, 31, 61, 1891.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 1891: a triangular number: 1 + 2 + … + 61 = 1891; a semiprime: 31 × 61, the product of two primes.
- 2
1891 is composite. Its prime factorisation is
- 3
The divisors add up to 1984; without 1891 itself that is 93, so 1891 is deficient (93 is less than 1891). Euler's totient φ(1891) = 1800 numbers up to 1891 share no factor with it.
- 4
The digits of 1891 add up to 19, and repeating that until one digit is left gives the digital root 1. The Collatz sequence (halve if even, else 3n+1) takes 37 steps to reach 1.
LaTeX source of the formulas on this page
\[ 1891 = 31 \times 61 \]
1891 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 4 |
| Sum of divisors | 1984 |
| Euler totient φ(n) | 1800 |
| Square | 3575881 |
| Cube | 6761990971 |
| Square root | 43.485630 |
| Digit sum / digital root | 19 / 1 |
| Collatz steps to 1 | 37 |
| Scientific notation | 1.891 × |
1891 in other forms
| Form | Value |
|---|---|
| In words | one thousand eight hundred and ninety-one |
| Roman numerals | MDCCCXCI |
| Binary (base 2) | 11101100011 |
| Octal (base 8) | 3543 |
| Hexadecimal (base 16) | 763 |
| Base 3 | 2121001 |
| As time | 1891 seconds = 31 min 31 s |
Is 1891 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 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 1) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 1) | 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 3) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 1) | 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 10) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | No (remainder 7) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 1891 a prime number?
No. 1891 = 31 × 61, so it is divisible by 31.
What are the factors of 1891?
1, 31, 61, 1891.
What is 1891 in binary?
11101100011 (hexadecimal 763, octal 3543).
What is the square root of 1891?
About 43.4856.
What is 1891 in Roman numerals?
MDCCCXCI.
Is 1891 divisible by 3?
No. Its digits add up to 19, which is not a multiple of 3.
What is special about the number 1891?
1891 is a triangular number: 1 + 2 + … + 61 = 1891; a semiprime: 31 × 61, the product of two primes.