The number 824
824 is a composite number with 8 divisors. Its prime factorisation is × 103. Divisors (8): 1, 2, 4, 8, 103, 206, 412, 824.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
824 has no famous special property in the usual lists (prime, square, cube, triangular, Fibonacci, palindrome, perfect), but it is still a composite number.
- 2
824 is composite. Its prime factorisation is
- 3
The divisors add up to 1560; without 824 itself that is 736, so 824 is deficient (736 is less than 824). Euler's totient φ(824) = 408 numbers up to 824 share no factor with it.
- 4
The digits of 824 add up to 14, and repeating that until one digit is left gives the digital root 5. The Collatz sequence (halve if even, else 3n+1) takes 90 steps to reach 1.
LaTeX source of the formulas on this page
\[ 824 = 2^{3} \times 103 \]824 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 8 |
| Sum of divisors | 1560 |
| Euler totient φ(n) | 408 |
| Square | 678976 |
| Cube | 559476224 |
| Square root | 28.705400 (= 2√206) |
| Digit sum / digital root | 14 / 5 |
| Collatz steps to 1 | 90 |
| Scientific notation | 8.24 × |
824 in other forms
| Form | Value |
|---|---|
| In words | eight hundred and twenty-four |
| Roman numerals | DCCCXXIV |
| Binary (base 2) | 1100111000 |
| Octal (base 8) | 1470 |
| Hexadecimal (base 16) | 338 |
| Base 3 | 1010112 |
| As time | 824 seconds = 13 min 44 s |
Is 824 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (824 ÷ 2 = 412) | 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 (824 ÷ 4 = 206) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | No (remainder 4) | 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 | No (remainder 5) | 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 | Yes (824 ÷ 8 = 103) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 5) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | No (remainder 4) | 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 8) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 824 a prime number?
No. 824 = × 103, so it is divisible by 2.
What are the factors of 824?
1, 2, 4, 8, 103, 206, 412, 824.
What is 824 in binary?
1100111000 (hexadecimal 338, octal 1470).
What is the square root of 824?
About 28.7054, exactly 2√206.
What is 824 in Roman numerals?
DCCCXXIV.
Is 824 divisible by 3?
No. Its digits add up to 14, which is not a multiple of 3.
What is special about the number 824?
It is a composite number with 8 divisors.