The number 3564
3564 is a composite number with 30 divisors. Its prime factorisation is × × 11. Divisors (30): 1, 2, 3, 4, 6, 9, 11, 12, 18, 22, 27, 33, 36, 44, 54, 66 … 3564.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 3564: a happy number: repeatedly adding the squares of its digits reaches 1; a Harshad number: divisible by its digit sum 18.
- 2
3564 is composite. Its prime factorisation is
- 3
The divisors add up to 10164; without 3564 itself that is 6600, so 3564 is abundant (6600 is more than 3564). Euler's totient φ(3564) = 1080 numbers up to 3564 share no factor with it.
- 4
The digits of 3564 add up to 18, and repeating that until one digit is left gives the digital root 9. The Collatz sequence (halve if even, else 3n+1) takes 48 steps to reach 1.
LaTeX source of the formulas on this page
\[ 3564 = 2^{2} \times 3^{4} \times 11 \]3564 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 30 |
| Sum of divisors | 10164 |
| Euler totient φ(n) | 1080 |
| Square | 12702096 |
| Cube | 45270270144 |
| Square root | 59.699246 (= 18√11) |
| Digit sum / digital root | 18 / 9 |
| Collatz steps to 1 | 48 |
| Scientific notation | 3.564 × |
3564 in other forms
| Form | Value |
|---|---|
| In words | three thousand five hundred and sixty-four |
| Roman numerals | MMMDLXIV |
| Binary (base 2) | 110111101100 |
| Octal (base 8) | 6754 |
| Hexadecimal (base 16) | DEC |
| Base 3 | 11220000 |
| As time | 3564 seconds = 59 min 24 s |
Is 3564 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (3564 ÷ 2 = 1782) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (3564 ÷ 3 = 1188) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (3564 ÷ 4 = 891) | 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 (3564 ÷ 6 = 594) | 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 | No (remainder 4) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | Yes (3564 ÷ 9 = 396) | 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 | Yes (3564 ÷ 11 = 324) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (3564 ÷ 12 = 297) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 3564 a prime number?
No. 3564 = × × 11, so it is divisible by 2.
What are the factors of 3564?
1, 2, 3, 4, 6, 9, 11, 12, 18, 22, 27, 33, 36, 44, 54, 66, 81, 99, 108, 132, 162, 198, 297, 324, 396, 594, 891, 1188, 1782, 3564.
What is 3564 in binary?
110111101100 (hexadecimal DEC, octal 6754).
What is the square root of 3564?
About 59.6992, exactly 18√11.
What is 3564 in Roman numerals?
MMMDLXIV.
Is 3564 divisible by 3?
Yes. Its digits add up to 18, a multiple of 3.
What is special about the number 3564?
3564 is a happy number: repeatedly adding the squares of its digits reaches 1; a Harshad number: divisible by its digit sum 18.