The number 47664
47664 is a composite number with 30 divisors. Its prime factorisation is × × 331. Divisors (30): 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 36, 48, 72, 144, 331 … 47664.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
47664 has no famous special property in the usual lists (prime, square, cube, triangular, Fibonacci, palindrome, perfect), but it is still a composite number.
- 2
47664 is composite. Its prime factorisation is
- 3
The divisors add up to 133796; without 47664 itself that is 86132, so 47664 is abundant (86132 is more than 47664). Euler's totient φ(47664) = 15840 numbers up to 47664 share no factor with it.
- 4
The digits of 47664 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 52 steps to reach 1.
LaTeX source of the formulas on this page
\[ 47664 = 2^{4} \times 3^{2} \times 331 \]47664 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 30 |
| Sum of divisors | 133796 |
| Euler totient φ(n) | 15840 |
| Square | 2271856896 |
| Cube | 108285787090944 |
| Square root | 218.320865 (= 12√331) |
| Digit sum / digital root | 27 / 9 |
| Collatz steps to 1 | 52 |
| Scientific notation | 4.7664 × |
47664 in other forms
| Form | Value |
|---|---|
| In words | forty-seven thousand six hundred and sixty-four |
| Binary (base 2) | 1011101000110000 |
| Octal (base 8) | 135060 |
| Hexadecimal (base 16) | BA30 |
| Base 3 | 2102101100 |
| As time | 47664 seconds = 13 h 14 min 24 s |
Is 47664 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (47664 ÷ 2 = 23832) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (47664 ÷ 3 = 15888) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (47664 ÷ 4 = 11916) | 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 (47664 ÷ 6 = 7944) | 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 (47664 ÷ 8 = 5958) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | Yes (47664 ÷ 9 = 5296) | 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 1) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (47664 ÷ 12 = 3972) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 47664 a prime number?
No. 47664 = × × 331, so it is divisible by 2.
What are the factors of 47664?
1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 36, 48, 72, 144, 331, 662, 993, 1324, 1986, 2648, 2979, 3972, 5296, 5958, 7944, 11916, 15888, 23832, 47664.
What is 47664 in binary?
1011101000110000 (hexadecimal BA30, octal 135060).
What is the square root of 47664?
About 218.3209, exactly 12√331.
Is 47664 divisible by 3?
Yes. Its digits add up to 27, a multiple of 3.
What is special about the number 47664?
It is a composite number with 30 divisors.