The number 49584
49584 is a composite number with 20 divisors. Its prime factorisation is × 3 × 1033. Divisors (20): 1, 2, 3, 4, 6, 8, 12, 16, 24, 48, 1033, 2066, 3099, 4132, 6198, 8264 … 49584.
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How to work it out
- 1
49584 has no famous special property in the usual lists (prime, square, cube, triangular, Fibonacci, palindrome, perfect), but it is still a composite number.
- 2
49584 is composite. Its prime factorisation is
- 3
The divisors add up to 128216; without 49584 itself that is 78632, so 49584 is abundant (78632 is more than 49584). Euler's totient φ(49584) = 16512 numbers up to 49584 share no factor with it.
- 4
The digits of 49584 add up to 30, and repeating that until one digit is left gives the digital root 3. The Collatz sequence (halve if even, else 3n+1) takes 140 steps to reach 1.
LaTeX source of the formulas on this page
\[ 49584 = 2^{4} \times 3 \times 1033 \]49584 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 20 |
| Sum of divisors | 128216 |
| Euler totient φ(n) | 16512 |
| Square | 2458573056 |
| Cube | 121905886408704 |
| Square root | 222.674651 (= 4√3099) |
| Digit sum / digital root | 30 / 3 |
| Collatz steps to 1 | 140 |
| Scientific notation | 4.9584 × |
49584 in other forms
| Form | Value |
|---|---|
| In words | forty-nine thousand five hundred and eighty-four |
| Binary (base 2) | 1100000110110000 |
| Octal (base 8) | 140660 |
| Hexadecimal (base 16) | C1B0 |
| Base 3 | 2112000110 |
| As time | 49584 seconds = 13 h 46 min 24 s |
Is 49584 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (49584 ÷ 2 = 24792) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (49584 ÷ 3 = 16528) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (49584 ÷ 4 = 12396) | 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 (49584 ÷ 6 = 8264) | 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 (49584 ÷ 8 = 6198) | 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 7) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (49584 ÷ 12 = 4132) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 49584 a prime number?
No. 49584 = × 3 × 1033, so it is divisible by 2.
What are the factors of 49584?
1, 2, 3, 4, 6, 8, 12, 16, 24, 48, 1033, 2066, 3099, 4132, 6198, 8264, 12396, 16528, 24792, 49584.
What is 49584 in binary?
1100000110110000 (hexadecimal C1B0, octal 140660).
What is the square root of 49584?
About 222.6747, exactly 4√3099.
Is 49584 divisible by 3?
Yes. Its digits add up to 30, a multiple of 3.
What is special about the number 49584?
It is a composite number with 20 divisors.