The number 42384
42384 is a composite number with 20 divisors. Its prime factorisation is × 3 × 883. Divisors (20): 1, 2, 3, 4, 6, 8, 12, 16, 24, 48, 883, 1766, 2649, 3532, 5298, 7064 … 42384.
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How to work it out
- 1
What is special about 42384: a happy number: repeatedly adding the squares of its digits reaches 1.
- 2
42384 is composite. Its prime factorisation is
- 3
The divisors add up to 109616; without 42384 itself that is 67232, so 42384 is abundant (67232 is more than 42384). Euler's totient φ(42384) = 14112 numbers up to 42384 share no factor with it.
- 4
The digits of 42384 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 101 steps to reach 1.
LaTeX source of the formulas on this page
\[ 42384 = 2^{4} \times 3 \times 883 \]42384 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 20 |
| Sum of divisors | 109616 |
| Euler totient φ(n) | 14112 |
| Square | 1796403456 |
| Cube | 76138764079104 |
| Square root | 205.873748 (= 4√2649) |
| Digit sum / digital root | 21 / 3 |
| Collatz steps to 1 | 101 |
| Scientific notation | 4.2384 × |
42384 in other forms
| Form | Value |
|---|---|
| In words | forty-two thousand three hundred and eighty-four |
| Binary (base 2) | 1010010110010000 |
| Octal (base 8) | 122620 |
| Hexadecimal (base 16) | A590 |
| Base 3 | 2011010210 |
| As time | 42384 seconds = 11 h 46 min 24 s |
Is 42384 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (42384 ÷ 2 = 21192) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (42384 ÷ 3 = 14128) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (42384 ÷ 4 = 10596) | 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 (42384 ÷ 6 = 7064) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 6) | 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 (42384 ÷ 8 = 5298) | 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 1) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (42384 ÷ 12 = 3532) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 42384 a prime number?
No. 42384 = × 3 × 883, so it is divisible by 2.
What are the factors of 42384?
1, 2, 3, 4, 6, 8, 12, 16, 24, 48, 883, 1766, 2649, 3532, 5298, 7064, 10596, 14128, 21192, 42384.
What is 42384 in binary?
1010010110010000 (hexadecimal A590, octal 122620).
What is the square root of 42384?
About 205.8737, exactly 4√2649.
Is 42384 divisible by 3?
Yes. Its digits add up to 21, a multiple of 3.
What is special about the number 42384?
42384 is a happy number: repeatedly adding the squares of its digits reaches 1.