The number 12564
12564 is a composite number with 18 divisors. Its prime factorisation is × × 349. Divisors (18): 1, 2, 3, 4, 6, 9, 12, 18, 36, 349, 698, 1047, 1396, 2094, 3141, 4188 … 12564.
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How to work it out
- 1
What is special about 12564: a happy number: repeatedly adding the squares of its digits reaches 1; a Harshad number: divisible by its digit sum 18.
- 2
12564 is composite. Its prime factorisation is
- 3
The divisors add up to 31850; without 12564 itself that is 19286, so 12564 is abundant (19286 is more than 12564). Euler's totient φ(12564) = 4176 numbers up to 12564 share no factor with it.
- 4
The digits of 12564 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 125 steps to reach 1.
LaTeX source of the formulas on this page
\[ 12564 = 2^{2} \times 3^{2} \times 349 \]12564 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 18 |
| Sum of divisors | 31850 |
| Euler totient φ(n) | 4176 |
| Square | 157854096 |
| Cube | 1983278862144 |
| Square root | 112.089250 (= 6√349) |
| Digit sum / digital root | 18 / 9 |
| Collatz steps to 1 | 125 |
| Scientific notation | 1.2564 × |
12564 in other forms
| Form | Value |
|---|---|
| In words | twelve thousand five hundred and sixty-four |
| Binary (base 2) | 11000100010100 |
| Octal (base 8) | 30424 |
| Hexadecimal (base 16) | 3114 |
| Base 3 | 122020100 |
| As time | 12564 seconds = 3 h 29 min 24 s |
Is 12564 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (12564 ÷ 2 = 6282) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (12564 ÷ 3 = 4188) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (12564 ÷ 4 = 3141) | 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 (12564 ÷ 6 = 2094) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 6) | 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 (12564 ÷ 9 = 1396) | 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 2) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (12564 ÷ 12 = 1047) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 12564 a prime number?
No. 12564 = × × 349, so it is divisible by 2.
What are the factors of 12564?
1, 2, 3, 4, 6, 9, 12, 18, 36, 349, 698, 1047, 1396, 2094, 3141, 4188, 6282, 12564.
What is 12564 in binary?
11000100010100 (hexadecimal 3114, octal 30424).
What is the square root of 12564?
About 112.0893, exactly 6√349.
Is 12564 divisible by 3?
Yes. Its digits add up to 18, a multiple of 3.
What is special about the number 12564?
12564 is a happy number: repeatedly adding the squares of its digits reaches 1; a Harshad number: divisible by its digit sum 18.