The number 24384
24384 is a composite number with 28 divisors. Its prime factorisation is × 3 × 127. Divisors (28): 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 64, 96, 127, 192, 254 … 24384.
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How to work it out
- 1
What is special about 24384: a happy number: repeatedly adding the squares of its digits reaches 1.
- 2
24384 is composite. Its prime factorisation is
- 3
The divisors add up to 65024; without 24384 itself that is 40640, so 24384 is abundant (40640 is more than 24384). Euler's totient φ(24384) = 8064 numbers up to 24384 share no factor with it.
- 4
The digits of 24384 add up to 21, and repeating that until one digit is left gives the digital root 3. The Collatz sequence (halve if even, else 3n+1) takes 113 steps to reach 1.
LaTeX source of the formulas on this page
\[ 24384 = 2^{6} \times 3 \times 127 \]24384 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 28 |
| Sum of divisors | 65024 |
| Euler totient φ(n) | 8064 |
| Square | 594579456 |
| Cube | 14498225455104 |
| Square root | 156.153770 (= 8√381) |
| Digit sum / digital root | 21 / 3 |
| Collatz steps to 1 | 113 |
| Scientific notation | 2.4384 × |
24384 in other forms
| Form | Value |
|---|---|
| In words | twenty-four thousand three hundred and eighty-four |
| Binary (base 2) | 101111101000000 |
| Octal (base 8) | 57500 |
| Hexadecimal (base 16) | 5F40 |
| Base 3 | 1020110010 |
| As time | 24384 seconds = 6 h 46 min 24 s |
Is 24384 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (24384 ÷ 2 = 12192) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (24384 ÷ 3 = 8128) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (24384 ÷ 4 = 6096) | 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 (24384 ÷ 6 = 4064) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 3) | 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 (24384 ÷ 8 = 3048) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 3) | 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 8) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (24384 ÷ 12 = 2032) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 24384 a prime number?
No. 24384 = × 3 × 127, so it is divisible by 2.
What are the factors of 24384?
1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 64, 96, 127, 192, 254, 381, 508, 762, 1016, 1524, 2032, 3048, 4064, 6096, 8128, 12192, 24384.
What is 24384 in binary?
101111101000000 (hexadecimal 5F40, octal 57500).
What is the square root of 24384?
About 156.1538, exactly 8√381.
Is 24384 divisible by 3?
Yes. Its digits add up to 21, a multiple of 3.
What is special about the number 24384?
24384 is a happy number: repeatedly adding the squares of its digits reaches 1.