The number 13563
13563 is a composite number with 12 divisors. Its prime factorisation is × 11 × 137. Divisors (12): 1, 3, 9, 11, 33, 99, 137, 411, 1233, 1507, 4521, 13563.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
13563 has no famous special property in the usual lists (prime, square, cube, triangular, Fibonacci, palindrome, perfect), but it is still a composite number.
- 2
13563 is composite. Its prime factorisation is
- 3
The divisors add up to 21528; without 13563 itself that is 7965, so 13563 is deficient (7965 is less than 13563). Euler's totient φ(13563) = 8160 numbers up to 13563 share no factor with it.
- 4
The digits of 13563 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 89 steps to reach 1.
LaTeX source of the formulas on this page
\[ 13563 = 3^{2} \times 11 \times 137 \]13563 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 12 |
| Sum of divisors | 21528 |
| Euler totient φ(n) | 8160 |
| Square | 183954969 |
| Cube | 2494981244547 |
| Square root | 116.460294 (= 3√1507) |
| Digit sum / digital root | 18 / 9 |
| Collatz steps to 1 | 89 |
| Scientific notation | 1.3563 × |
13563 in other forms
| Form | Value |
|---|---|
| In words | thirteen thousand five hundred and sixty-three |
| Binary (base 2) | 11010011111011 |
| Octal (base 8) | 32373 |
| Hexadecimal (base 16) | 34FB |
| Base 3 | 200121100 |
| As time | 13563 seconds = 3 h 46 min 3 s |
Is 13563 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | No (remainder 1) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (13563 ÷ 3 = 4521) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | No (remainder 3) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | No (remainder 3) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | No (remainder 3) | 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 3) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | Yes (13563 ÷ 9 = 1507) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | No (remainder 3) | A number is divisible by 10 if the last digit is 0. |
| 11 | Yes (13563 ÷ 11 = 1233) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | No (remainder 3) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 13563 a prime number?
No. 13563 = × 11 × 137, so it is divisible by 3.
What are the factors of 13563?
1, 3, 9, 11, 33, 99, 137, 411, 1233, 1507, 4521, 13563.
What is 13563 in binary?
11010011111011 (hexadecimal 34FB, octal 32373).
What is the square root of 13563?
About 116.4603, exactly 3√1507.
Is 13563 divisible by 3?
Yes. Its digits add up to 18, a multiple of 3.
What is special about the number 13563?
It is a composite number with 12 divisors.