The number 49824
49824 is a composite number with 36 divisors. Its prime factorisation is × × 173. Divisors (36): 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 32, 36, 48, 72, 96 … 49824.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
49824 has no famous special property in the usual lists (prime, square, cube, triangular, Fibonacci, palindrome, perfect), but it is still a composite number.
- 2
49824 is composite. Its prime factorisation is
- 3
The divisors add up to 142506; without 49824 itself that is 92682, so 49824 is abundant (92682 is more than 49824). Euler's totient φ(49824) = 16512 numbers up to 49824 share no factor with it.
- 4
The digits of 49824 add up to 27, and repeating that until one digit is left gives the digital root 9. The Collatz sequence (halve if even, else 3n+1) takes 127 steps to reach 1.
LaTeX source of the formulas on this page
\[ 49824 = 2^{5} \times 3^{2} \times 173 \]49824 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 36 |
| Sum of divisors | 142506 |
| Euler totient φ(n) | 16512 |
| Square | 2482430976 |
| Cube | 123684640948224 |
| Square root | 223.212903 (= 12√346) |
| Digit sum / digital root | 27 / 9 |
| Collatz steps to 1 | 127 |
| Scientific notation | 4.9824 × |
49824 in other forms
| Form | Value |
|---|---|
| In words | forty-nine thousand eight hundred and twenty-four |
| Binary (base 2) | 1100001010100000 |
| Octal (base 8) | 141240 |
| Hexadecimal (base 16) | C2A0 |
| Base 3 | 2112100100 |
| As time | 49824 seconds = 13 h 50 min 24 s |
Is 49824 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (49824 ÷ 2 = 24912) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (49824 ÷ 3 = 16608) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (49824 ÷ 4 = 12456) | 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 (49824 ÷ 6 = 8304) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 5) | 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 (49824 ÷ 8 = 6228) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | Yes (49824 ÷ 9 = 5536) | 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 (49824 ÷ 12 = 4152) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 49824 a prime number?
No. 49824 = × × 173, so it is divisible by 2.
What are the factors of 49824?
1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 32, 36, 48, 72, 96, 144, 173, 288, 346, 519, 692, 1038, 1384, 1557, 2076, 2768, 3114, 4152, 5536, 6228, 8304, 12456, 16608, 24912, 49824.
What is 49824 in binary?
1100001010100000 (hexadecimal C2A0, octal 141240).
What is the square root of 49824?
About 223.2129, exactly 12√346.
Is 49824 divisible by 3?
Yes. Its digits add up to 27, a multiple of 3.
What is special about the number 49824?
It is a composite number with 36 divisors.