The number 21564
21564 is a composite number with 18 divisors. Its prime factorisation is × × 599. Divisors (18): 1, 2, 3, 4, 6, 9, 12, 18, 36, 599, 1198, 1797, 2396, 3594, 5391, 7188 … 21564.
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How to work it out
- 1
What is special about 21564: a happy number: repeatedly adding the squares of its digits reaches 1; a Harshad number: divisible by its digit sum 18.
- 2
21564 is composite. Its prime factorisation is
- 3
The divisors add up to 54600; without 21564 itself that is 33036, so 21564 is abundant (33036 is more than 21564). Euler's totient φ(21564) = 7176 numbers up to 21564 share no factor with it.
- 4
The digits of 21564 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 30 steps to reach 1.
LaTeX source of the formulas on this page
\[ 21564 = 2^{2} \times 3^{2} \times 599 \]21564 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 18 |
| Sum of divisors | 54600 |
| Euler totient φ(n) | 7176 |
| Square | 465006096 |
| Cube | 10027391454144 |
| Square root | 146.846859 (= 6√599) |
| Digit sum / digital root | 18 / 9 |
| Collatz steps to 1 | 30 |
| Scientific notation | 2.1564 × |
21564 in other forms
| Form | Value |
|---|---|
| In words | twenty-one thousand five hundred and sixty-four |
| Binary (base 2) | 101010000111100 |
| Octal (base 8) | 52074 |
| Hexadecimal (base 16) | 543C |
| Base 3 | 1002120200 |
| As time | 21564 seconds = 5 h 59 min 24 s |
Is 21564 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (21564 ÷ 2 = 10782) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (21564 ÷ 3 = 7188) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (21564 ÷ 4 = 5391) | 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 (21564 ÷ 6 = 3594) | 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 | Yes (21564 ÷ 9 = 2396) | 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 4) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (21564 ÷ 12 = 1797) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 21564 a prime number?
No. 21564 = × × 599, so it is divisible by 2.
What are the factors of 21564?
1, 2, 3, 4, 6, 9, 12, 18, 36, 599, 1198, 1797, 2396, 3594, 5391, 7188, 10782, 21564.
What is 21564 in binary?
101010000111100 (hexadecimal 543C, octal 52074).
What is the square root of 21564?
About 146.8469, exactly 6√599.
Is 21564 divisible by 3?
Yes. Its digits add up to 18, a multiple of 3.
What is special about the number 21564?
21564 is a happy number: repeatedly adding the squares of its digits reaches 1; a Harshad number: divisible by its digit sum 18.