The number 47328
47328 is a composite number with 48 divisors. Its prime factorisation is × 3 × 17 × 29. Divisors (48): 1, 2, 3, 4, 6, 8, 12, 16, 17, 24, 29, 32, 34, 48, 51, 58 … 47328.
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How to work it out
- 1
What is special about 47328: a Harshad number: divisible by its digit sum 24.
- 2
47328 is composite. Its prime factorisation is
- 3
The divisors add up to 136080; without 47328 itself that is 88752, so 47328 is abundant (88752 is more than 47328). Euler's totient φ(47328) = 14336 numbers up to 47328 share no factor with it.
- 4
The digits of 47328 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 101 steps to reach 1.
LaTeX source of the formulas on this page
\[ 47328 = 2^{5} \times 3 \times 17 \times 29 \]47328 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 48 |
| Sum of divisors | 136080 |
| Euler totient φ(n) | 14336 |
| Square | 2239939584 |
| Cube | 106011860631552 |
| Square root | 217.549994 (= 4√2958) |
| Digit sum / digital root | 24 / 6 |
| Collatz steps to 1 | 101 |
| Scientific notation | 4.7328 × |
47328 in other forms
| Form | Value |
|---|---|
| In words | forty-seven thousand three hundred and twenty-eight |
| Binary (base 2) | 1011100011100000 |
| Octal (base 8) | 134340 |
| Hexadecimal (base 16) | B8E0 |
| Base 3 | 2101220220 |
| As time | 47328 seconds = 13 h 8 min 48 s |
Is 47328 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (47328 ÷ 2 = 23664) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (47328 ÷ 3 = 15776) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (47328 ÷ 4 = 11832) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | No (remainder 3) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (47328 ÷ 6 = 7888) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 1) | 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 (47328 ÷ 8 = 5916) | 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 8) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 6) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (47328 ÷ 12 = 3944) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 47328 a prime number?
No. 47328 = × 3 × 17 × 29, so it is divisible by 2.
What are the factors of 47328?
1, 2, 3, 4, 6, 8, 12, 16, 17, 24, 29, 32, 34, 48, 51, 58, 68, 87, 96, 102, 116, 136, 174, 204, 232, 272, 348, 408, 464, 493, 544, 696, 816, 928, 986, 1392, 1479, 1632, 1972, 2784, 2958, 3944, 5916, 7888, 11832, 15776, 23664, 47328.
What is 47328 in binary?
1011100011100000 (hexadecimal B8E0, octal 134340).
What is the square root of 47328?
About 217.5500, exactly 4√2958.
Is 47328 divisible by 3?
Yes. Its digits add up to 24, a multiple of 3.
What is special about the number 47328?
47328 is a Harshad number: divisible by its digit sum 24.