The number 820
820 is a triangular number: 1 + 2 + … + 40 = 820. Its prime factorisation is × 5 × 41. Divisors (12): 1, 2, 4, 5, 10, 20, 41, 82, 164, 205, 410, 820.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 820: a triangular number: 1 + 2 + … + 40 = 820; a happy number: repeatedly adding the squares of its digits reaches 1; a Harshad number: divisible by its digit sum 10.
- 2
820 is composite. Its prime factorisation is
- 3
The divisors add up to 1764; without 820 itself that is 944, so 820 is abundant (944 is more than 820). Euler's totient φ(820) = 320 numbers up to 820 share no factor with it.
- 4
The digits of 820 add up to 10, and repeating that until one digit is left gives the digital root 1. The Collatz sequence (halve if even, else 3n+1) takes 28 steps to reach 1.
LaTeX source of the formulas on this page
\[ 820 = 2^{2} \times 5 \times 41 \]820 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 12 |
| Sum of divisors | 1764 |
| Euler totient φ(n) | 320 |
| Square | 672400 |
| Cube | 551368000 |
| Square root | 28.635642 (= 2√205) |
| Digit sum / digital root | 10 / 1 |
| Collatz steps to 1 | 28 |
| Scientific notation | 8.2 × |
820 in other forms
| Form | Value |
|---|---|
| In words | eight hundred and twenty |
| Roman numerals | DCCCXX |
| Binary (base 2) | 1100110100 |
| Octal (base 8) | 1464 |
| Hexadecimal (base 16) | 334 |
| Base 3 | 1010101 |
| As time | 820 seconds = 13 min 40 s |
Is 820 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (820 ÷ 2 = 410) | 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 | Yes (820 ÷ 4 = 205) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | Yes (820 ÷ 5 = 164) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | No (remainder 4) | 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 4) | 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 | Yes (820 ÷ 10 = 82) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 6) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | No (remainder 4) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 820 a prime number?
No. 820 = × 5 × 41, so it is divisible by 2.
What are the factors of 820?
1, 2, 4, 5, 10, 20, 41, 82, 164, 205, 410, 820.
What is 820 in binary?
1100110100 (hexadecimal 334, octal 1464).
What is the square root of 820?
About 28.6356, exactly 2√205.
What is 820 in Roman numerals?
DCCCXX.
Is 820 divisible by 3?
No. Its digits add up to 10, which is not a multiple of 3.
What is special about the number 820?
820 is a triangular number: 1 + 2 + … + 40 = 820; a happy number: repeatedly adding the squares of its digits reaches 1; a Harshad number: divisible by its digit sum 10.