The number 1820
1820 is a composite number with 24 divisors. Its prime factorisation is × 5 × 7 × 13. Divisors (24): 1, 2, 4, 5, 7, 10, 13, 14, 20, 26, 28, 35, 52, 65, 70, 91 … 1820.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
1820 has no famous special property in the usual lists (prime, square, cube, triangular, Fibonacci, palindrome, perfect), but it is still a composite number.
- 2
1820 is composite. Its prime factorisation is
- 3
The divisors add up to 4704; without 1820 itself that is 2884, so 1820 is abundant (2884 is more than 1820). Euler's totient φ(1820) = 576 numbers up to 1820 share no factor with it.
- 4
The digits of 1820 add up to 11, and repeating that until one digit is left gives the digital root 2. The Collatz sequence (halve if even, else 3n+1) takes 42 steps to reach 1.
LaTeX source of the formulas on this page
\[ 1820 = 2^{2} \times 5 \times 7 \times 13 \]1820 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 24 |
| Sum of divisors | 4704 |
| Euler totient φ(n) | 576 |
| Square | 3312400 |
| Cube | 6028568000 |
| Square root | 42.661458 (= 2√455) |
| Digit sum / digital root | 11 / 2 |
| Collatz steps to 1 | 42 |
| Scientific notation | 1.82 × |
1820 in other forms
| Form | Value |
|---|---|
| In words | one thousand eight hundred and twenty |
| Roman numerals | MDCCCXX |
| Binary (base 2) | 11100011100 |
| Octal (base 8) | 3434 |
| Hexadecimal (base 16) | 71C |
| Base 3 | 2111102 |
| As time | 1820 seconds = 30 min 20 s |
Is 1820 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (1820 ÷ 2 = 910) | 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 | Yes (1820 ÷ 4 = 455) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | Yes (1820 ÷ 5 = 364) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | No (remainder 2) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | Yes (1820 ÷ 7 = 260) | 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 4) | 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 | Yes (1820 ÷ 10 = 182) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 5) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | No (remainder 8) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 1820 a prime number?
No. 1820 = × 5 × 7 × 13, so it is divisible by 2.
What are the factors of 1820?
1, 2, 4, 5, 7, 10, 13, 14, 20, 26, 28, 35, 52, 65, 70, 91, 130, 140, 182, 260, 364, 455, 910, 1820.
What is 1820 in binary?
11100011100 (hexadecimal 71C, octal 3434).
What is the square root of 1820?
About 42.6615, exactly 2√455.
What is 1820 in Roman numerals?
MDCCCXX.
Is 1820 divisible by 3?
No. Its digits add up to 11, which is not a multiple of 3.
What is special about the number 1820?
It is a composite number with 24 divisors.