The number 24084
24084 is a composite number with 24 divisors. Its prime factorisation is × × 223. Divisors (24): 1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 54, 108, 223, 446, 669, 892 … 24084.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 24084: a happy number: repeatedly adding the squares of its digits reaches 1; a Harshad number: divisible by its digit sum 18.
- 2
24084 is composite. Its prime factorisation is
- 3
The divisors add up to 62720; without 24084 itself that is 38636, so 24084 is abundant (38636 is more than 24084). Euler's totient φ(24084) = 7992 numbers up to 24084 share no factor with it.
- 4
The digits of 24084 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 43 steps to reach 1.
LaTeX source of the formulas on this page
\[ 24084 = 2^{2} \times 3^{3} \times 223 \]24084 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 24 |
| Sum of divisors | 62720 |
| Euler totient φ(n) | 7992 |
| Square | 580039056 |
| Cube | 13969660624704 |
| Square root | 155.190206 (= 6√669) |
| Digit sum / digital root | 18 / 9 |
| Collatz steps to 1 | 43 |
| Scientific notation | 2.4084 × |
24084 in other forms
| Form | Value |
|---|---|
| In words | twenty-four thousand and eighty-four |
| Binary (base 2) | 101111000010100 |
| Octal (base 8) | 57024 |
| Hexadecimal (base 16) | 5E14 |
| Base 3 | 1020001000 |
| As time | 24084 seconds = 6 h 41 min 24 s |
Is 24084 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (24084 ÷ 2 = 12042) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (24084 ÷ 3 = 8028) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (24084 ÷ 4 = 6021) | 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 (24084 ÷ 6 = 4014) | 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 | No (remainder 4) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | Yes (24084 ÷ 9 = 2676) | 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 5) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (24084 ÷ 12 = 2007) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 24084 a prime number?
No. 24084 = × × 223, so it is divisible by 2.
What are the factors of 24084?
1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 54, 108, 223, 446, 669, 892, 1338, 2007, 2676, 4014, 6021, 8028, 12042, 24084.
What is 24084 in binary?
101111000010100 (hexadecimal 5E14, octal 57024).
What is the square root of 24084?
About 155.1902, exactly 6√669.
Is 24084 divisible by 3?
Yes. Its digits add up to 18, a multiple of 3.
What is special about the number 24084?
24084 is a happy number: repeatedly adding the squares of its digits reaches 1; a Harshad number: divisible by its digit sum 18.