The number 1890
1890 is a composite number with 32 divisors. Its prime factorisation is 2 × × 5 × 7. Divisors (32): 1, 2, 3, 5, 6, 7, 9, 10, 14, 15, 18, 21, 27, 30, 35, 42 … 1890.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 1890: a Harshad number: divisible by its digit sum 18.
- 2
1890 is composite. Its prime factorisation is
- 3
The divisors add up to 5760; without 1890 itself that is 3870, so 1890 is abundant (3870 is more than 1890). Euler's totient φ(1890) = 432 numbers up to 1890 share no factor with it.
- 4
The digits of 1890 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 37 steps to reach 1.
LaTeX source of the formulas on this page
\[ 1890 = 2 \times 3^{3} \times 5 \times 7 \]1890 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 32 |
| Sum of divisors | 5760 |
| Euler totient φ(n) | 432 |
| Square | 3572100 |
| Cube | 6751269000 |
| Square root | 43.474130 (= 3√210) |
| Digit sum / digital root | 18 / 9 |
| Collatz steps to 1 | 37 |
| Scientific notation | 1.89 × |
1890 in other forms
| Form | Value |
|---|---|
| In words | one thousand eight hundred and ninety |
| Roman numerals | MDCCCXC |
| Binary (base 2) | 11101100010 |
| Octal (base 8) | 3542 |
| Hexadecimal (base 16) | 762 |
| Base 3 | 2121000 |
| As time | 1890 seconds = 31 min 30 s |
Is 1890 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (1890 ÷ 2 = 945) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (1890 ÷ 3 = 630) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | No (remainder 2) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | Yes (1890 ÷ 5 = 378) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (1890 ÷ 6 = 315) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | Yes (1890 ÷ 7 = 270) | 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 2) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | Yes (1890 ÷ 9 = 210) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | Yes (1890 ÷ 10 = 189) | 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 6) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 1890 a prime number?
No. 1890 = 2 × × 5 × 7, so it is divisible by 2.
What are the factors of 1890?
1, 2, 3, 5, 6, 7, 9, 10, 14, 15, 18, 21, 27, 30, 35, 42, 45, 54, 63, 70, 90, 105, 126, 135, 189, 210, 270, 315, 378, 630, 945, 1890.
What is 1890 in binary?
11101100010 (hexadecimal 762, octal 3542).
What is the square root of 1890?
About 43.4741, exactly 3√210.
What is 1890 in Roman numerals?
MDCCCXC.
Is 1890 divisible by 3?
Yes. Its digits add up to 18, a multiple of 3.
What is special about the number 1890?
1890 is a Harshad number: divisible by its digit sum 18.