The number 564
564 is a composite number with 12 divisors. Its prime factorisation is × 3 × 47. Divisors (12): 1, 2, 3, 4, 6, 12, 47, 94, 141, 188, 282, 564.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
564 has no famous special property in the usual lists (prime, square, cube, triangular, Fibonacci, palindrome, perfect), but it is still a composite number.
- 2
564 is composite. Its prime factorisation is
- 3
The divisors add up to 1344; without 564 itself that is 780, so 564 is abundant (780 is more than 564). Euler's totient φ(564) = 184 numbers up to 564 share no factor with it.
- 4
The digits of 564 add up to 15, and repeating that until one digit is left gives the digital root 6. The Collatz sequence (halve if even, else 3n+1) takes 17 steps to reach 1.
LaTeX source of the formulas on this page
\[ 564 = 2^{2} \times 3 \times 47 \]564 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 12 |
| Sum of divisors | 1344 |
| Euler totient φ(n) | 184 |
| Square | 318096 |
| Cube | 179406144 |
| Square root | 23.748684 (= 2√141) |
| Digit sum / digital root | 15 / 6 |
| Collatz steps to 1 | 17 |
| Scientific notation | 5.64 × |
564 in other forms
| Form | Value |
|---|---|
| In words | five hundred and sixty-four |
| Roman numerals | DLXIV |
| Binary (base 2) | 1000110100 |
| Octal (base 8) | 1064 |
| Hexadecimal (base 16) | 234 |
| Base 3 | 202220 |
| As time | 564 seconds = 9 min 24 s |
Is 564 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (564 ÷ 2 = 282) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (564 ÷ 3 = 188) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (564 ÷ 4 = 141) | 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 (564 ÷ 6 = 94) | 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 | No (remainder 4) | 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 3) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (564 ÷ 12 = 47) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 564 a prime number?
No. 564 = × 3 × 47, so it is divisible by 2.
What are the factors of 564?
1, 2, 3, 4, 6, 12, 47, 94, 141, 188, 282, 564.
What is 564 in binary?
1000110100 (hexadecimal 234, octal 1064).
What is the square root of 564?
About 23.7487, exactly 2√141.
What is 564 in Roman numerals?
DLXIV.
Is 564 divisible by 3?
Yes. Its digits add up to 15, a multiple of 3.
What is special about the number 564?
It is a composite number with 12 divisors.