The number 828
828 is a palindrome: it reads 828 backwards too. Its prime factorisation is × × 23. Divisors (18): 1, 2, 3, 4, 6, 9, 12, 18, 23, 36, 46, 69, 92, 138, 207, 276 … 828.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 828: a palindrome: it reads 828 backwards too; a Harshad number: divisible by its digit sum 18.
- 2
828 is composite. Its prime factorisation is
- 3
The divisors add up to 2184; without 828 itself that is 1356, so 828 is abundant (1356 is more than 828). Euler's totient φ(828) = 264 numbers up to 828 share no factor with it.
- 4
The digits of 828 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 90 steps to reach 1.
LaTeX source of the formulas on this page
\[ 828 = 2^{2} \times 3^{2} \times 23 \]828 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 18 |
| Sum of divisors | 2184 |
| Euler totient φ(n) | 264 |
| Square | 685584 |
| Cube | 567663552 |
| Square root | 28.774989 (= 6√23) |
| Digit sum / digital root | 18 / 9 |
| Collatz steps to 1 | 90 |
| Scientific notation | 8.28 × |
828 in other forms
| Form | Value |
|---|---|
| In words | eight hundred and twenty-eight |
| Roman numerals | DCCCXXVIII |
| Binary (base 2) | 1100111100 |
| Octal (base 8) | 1474 |
| Hexadecimal (base 16) | 33C |
| Base 3 | 1010200 |
| As time | 828 seconds = 13 min 48 s |
Is 828 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (828 ÷ 2 = 414) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (828 ÷ 3 = 276) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (828 ÷ 4 = 207) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | No (remainder 3) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (828 ÷ 6 = 138) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 2) | 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 | Yes (828 ÷ 9 = 92) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | No (remainder 8) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 3) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (828 ÷ 12 = 69) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 828 a prime number?
No. 828 = × × 23, so it is divisible by 2.
What are the factors of 828?
1, 2, 3, 4, 6, 9, 12, 18, 23, 36, 46, 69, 92, 138, 207, 276, 414, 828.
What is 828 in binary?
1100111100 (hexadecimal 33C, octal 1474).
What is the square root of 828?
About 28.7750, exactly 6√23.
What is 828 in Roman numerals?
DCCCXXVIII.
Is 828 divisible by 3?
Yes. Its digits add up to 18, a multiple of 3.
What is special about the number 828?
828 is a palindrome: it reads 828 backwards too; a Harshad number: divisible by its digit sum 18.