The number 5664
5664 is a composite number with 24 divisors. Its prime factorisation is × 3 × 59. Divisors (24): 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 59, 96, 118, 177, 236 … 5664.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
5664 has no famous special property in the usual lists (prime, square, cube, triangular, Fibonacci, palindrome, perfect), but it is still a composite number.
- 2
5664 is composite. Its prime factorisation is
- 3
The divisors add up to 15120; without 5664 itself that is 9456, so 5664 is abundant (9456 is more than 5664). Euler's totient φ(5664) = 1856 numbers up to 5664 share no factor with it.
- 4
The digits of 5664 add up to 21, and repeating that until one digit is left gives the digital root 3. The Collatz sequence (halve if even, else 3n+1) takes 36 steps to reach 1.
LaTeX source of the formulas on this page
\[ 5664 = 2^{5} \times 3 \times 59 \]5664 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 24 |
| Sum of divisors | 15120 |
| Euler totient φ(n) | 1856 |
| Square | 32080896 |
| Cube | 181706194944 |
| Square root | 75.259551 (= 4√354) |
| Digit sum / digital root | 21 / 3 |
| Collatz steps to 1 | 36 |
| Scientific notation | 5.664 × |
5664 in other forms
| Form | Value |
|---|---|
| In words | five thousand six hundred and sixty-four |
| Binary (base 2) | 1011000100000 |
| Octal (base 8) | 13040 |
| Hexadecimal (base 16) | 1620 |
| Base 3 | 21202210 |
| As time | 5664 seconds = 1 h 34 min 24 s |
Is 5664 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (5664 ÷ 2 = 2832) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (5664 ÷ 3 = 1888) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (5664 ÷ 4 = 1416) | 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 (5664 ÷ 6 = 944) | 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 (5664 ÷ 8 = 708) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 3) | 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 10) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (5664 ÷ 12 = 472) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 5664 a prime number?
No. 5664 = × 3 × 59, so it is divisible by 2.
What are the factors of 5664?
1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 59, 96, 118, 177, 236, 354, 472, 708, 944, 1416, 1888, 2832, 5664.
What is 5664 in binary?
1011000100000 (hexadecimal 1620, octal 13040).
What is the square root of 5664?
About 75.2596, exactly 4√354.
Is 5664 divisible by 3?
Yes. Its digits add up to 21, a multiple of 3.
What is special about the number 5664?
It is a composite number with 24 divisors.