The number 47824
47824 is a composite number with 30 divisors. Its prime factorisation is × × 61. Divisors (30): 1, 2, 4, 7, 8, 14, 16, 28, 49, 56, 61, 98, 112, 122, 196, 244 … 47824.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
47824 has no famous special property in the usual lists (prime, square, cube, triangular, Fibonacci, palindrome, perfect), but it is still a composite number.
- 2
47824 is composite. Its prime factorisation is
- 3
The divisors add up to 109554; without 47824 itself that is 61730, so 47824 is abundant (61730 is more than 47824). Euler's totient φ(47824) = 20160 numbers up to 47824 share no factor with it.
- 4
The digits of 47824 add up to 25, and repeating that until one digit is left gives the digital root 7. The Collatz sequence (halve if even, else 3n+1) takes 52 steps to reach 1.
LaTeX source of the formulas on this page
\[ 47824 = 2^{4} \times 7^{2} \times 61 \]47824 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 30 |
| Sum of divisors | 109554 |
| Euler totient φ(n) | 20160 |
| Square | 2287134976 |
| Cube | 109379943092224 |
| Square root | 218.686991 (= 28√61) |
| Digit sum / digital root | 25 / 7 |
| Collatz steps to 1 | 52 |
| Scientific notation | 4.7824 × |
47824 in other forms
| Form | Value |
|---|---|
| In words | forty-seven thousand eight hundred and twenty-four |
| Binary (base 2) | 1011101011010000 |
| Octal (base 8) | 135320 |
| Hexadecimal (base 16) | BAD0 |
| Base 3 | 2102121021 |
| As time | 47824 seconds = 13 h 17 min 4 s |
Is 47824 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (47824 ÷ 2 = 23912) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | No (remainder 1) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (47824 ÷ 4 = 11956) | 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 | No (remainder 4) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | Yes (47824 ÷ 7 = 6832) | 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 (47824 ÷ 8 = 5978) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 7) | 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 | No (remainder 4) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 47824 a prime number?
No. 47824 = × × 61, so it is divisible by 2.
What are the factors of 47824?
1, 2, 4, 7, 8, 14, 16, 28, 49, 56, 61, 98, 112, 122, 196, 244, 392, 427, 488, 784, 854, 976, 1708, 2989, 3416, 5978, 6832, 11956, 23912, 47824.
What is 47824 in binary?
1011101011010000 (hexadecimal BAD0, octal 135320).
What is the square root of 47824?
About 218.6870, exactly 28√61.
Is 47824 divisible by 3?
No. Its digits add up to 25, which is not a multiple of 3.
What is special about the number 47824?
It is a composite number with 30 divisors.