The number 47184
47184 is a composite number with 20 divisors. Its prime factorisation is × 3 × 983. Divisors (20): 1, 2, 3, 4, 6, 8, 12, 16, 24, 48, 983, 1966, 2949, 3932, 5898, 7864 … 47184.
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How to work it out
- 1
What is special about 47184: a Harshad number: divisible by its digit sum 24.
- 2
47184 is composite. Its prime factorisation is
- 3
The divisors add up to 122016; without 47184 itself that is 74832, so 47184 is abundant (74832 is more than 47184). Euler's totient φ(47184) = 15712 numbers up to 47184 share no factor with it.
- 4
The digits of 47184 add up to 24, and repeating that until one digit is left gives the digital root 6. The Collatz sequence (halve if even, else 3n+1) takes 145 steps to reach 1.
LaTeX source of the formulas on this page
\[ 47184 = 2^{4} \times 3 \times 983 \]47184 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 20 |
| Sum of divisors | 122016 |
| Euler totient φ(n) | 15712 |
| Square | 2226329856 |
| Cube | 105047147925504 |
| Square root | 217.218784 (= 4√2949) |
| Digit sum / digital root | 24 / 6 |
| Collatz steps to 1 | 145 |
| Scientific notation | 4.7184 × |
47184 in other forms
| Form | Value |
|---|---|
| In words | forty-seven thousand one hundred and eighty-four |
| Binary (base 2) | 1011100001010000 |
| Octal (base 8) | 134120 |
| Hexadecimal (base 16) | B850 |
| Base 3 | 2101201120 |
| As time | 47184 seconds = 13 h 6 min 24 s |
Is 47184 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (47184 ÷ 2 = 23592) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (47184 ÷ 3 = 15728) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (47184 ÷ 4 = 11796) | 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 (47184 ÷ 6 = 7864) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 4) | 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 (47184 ÷ 8 = 5898) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 6) | 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 (47184 ÷ 12 = 3932) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 47184 a prime number?
No. 47184 = × 3 × 983, so it is divisible by 2.
What are the factors of 47184?
1, 2, 3, 4, 6, 8, 12, 16, 24, 48, 983, 1966, 2949, 3932, 5898, 7864, 11796, 15728, 23592, 47184.
What is 47184 in binary?
1011100001010000 (hexadecimal B850, octal 134120).
What is the square root of 47184?
About 217.2188, exactly 4√2949.
Is 47184 divisible by 3?
Yes. Its digits add up to 24, a multiple of 3.
What is special about the number 47184?
47184 is a Harshad number: divisible by its digit sum 24.