The number 1824
1824 is a composite number with 24 divisors. Its prime factorisation is × 3 × 19. Divisors (24): 1, 2, 3, 4, 6, 8, 12, 16, 19, 24, 32, 38, 48, 57, 76, 96 … 1824.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
1824 has no famous special property in the usual lists (prime, square, cube, triangular, Fibonacci, palindrome, perfect), but it is still a composite number.
- 2
1824 is composite. Its prime factorisation is
- 3
The divisors add up to 5040; without 1824 itself that is 3216, so 1824 is abundant (3216 is more than 1824). Euler's totient φ(1824) = 576 numbers up to 1824 share no factor with it.
- 4
The digits of 1824 add up to 15, and repeating that until one digit is left gives the digital root 6. The Collatz sequence (halve if even, else 3n+1) takes 37 steps to reach 1.
LaTeX source of the formulas on this page
\[ 1824 = 2^{5} \times 3 \times 19 \]1824 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 24 |
| Sum of divisors | 5040 |
| Euler totient φ(n) | 576 |
| Square | 3326976 |
| Cube | 6068404224 |
| Square root | 42.708313 (= 4√114) |
| Digit sum / digital root | 15 / 6 |
| Collatz steps to 1 | 37 |
| Scientific notation | 1.824 × |
1824 in other forms
| Form | Value |
|---|---|
| In words | one thousand eight hundred and twenty-four |
| Roman numerals | MDCCCXXIV |
| Binary (base 2) | 11100100000 |
| Octal (base 8) | 3440 |
| Hexadecimal (base 16) | 720 |
| Base 3 | 2111120 |
| As time | 1824 seconds = 30 min 24 s |
Is 1824 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (1824 ÷ 2 = 912) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (1824 ÷ 3 = 608) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (1824 ÷ 4 = 456) | 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 | Yes (1824 ÷ 6 = 304) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 4) | 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 (1824 ÷ 8 = 228) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 6) | 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 9) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (1824 ÷ 12 = 152) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 1824 a prime number?
No. 1824 = × 3 × 19, so it is divisible by 2.
What are the factors of 1824?
1, 2, 3, 4, 6, 8, 12, 16, 19, 24, 32, 38, 48, 57, 76, 96, 114, 152, 228, 304, 456, 608, 912, 1824.
What is 1824 in binary?
11100100000 (hexadecimal 720, octal 3440).
What is the square root of 1824?
About 42.7083, exactly 4√114.
What is 1824 in Roman numerals?
MDCCCXXIV.
Is 1824 divisible by 3?
Yes. Its digits add up to 15, a multiple of 3.
What is special about the number 1824?
It is a composite number with 24 divisors.