The number 13536
13536 is a composite number with 36 divisors. Its prime factorisation is × × 47. Divisors (36): 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 32, 36, 47, 48, 72 … 13536.
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How to work it out
- 1
What is special about 13536: a Harshad number: divisible by its digit sum 18.
- 2
13536 is composite. Its prime factorisation is
- 3
The divisors add up to 39312; without 13536 itself that is 25776, so 13536 is abundant (25776 is more than 13536). Euler's totient φ(13536) = 4416 numbers up to 13536 share no factor with it.
- 4
The digits of 13536 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 37 steps to reach 1.
LaTeX source of the formulas on this page
\[ 13536 = 2^{5} \times 3^{2} \times 47 \]13536 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 36 |
| Sum of divisors | 39312 |
| Euler totient φ(n) | 4416 |
| Square | 183223296 |
| Cube | 2480110534656 |
| Square root | 116.344317 (= 12√94) |
| Digit sum / digital root | 18 / 9 |
| Collatz steps to 1 | 37 |
| Scientific notation | 1.3536 × |
13536 in other forms
| Form | Value |
|---|---|
| In words | thirteen thousand five hundred and thirty-six |
| Binary (base 2) | 11010011100000 |
| Octal (base 8) | 32340 |
| Hexadecimal (base 16) | 34E0 |
| Base 3 | 200120100 |
| As time | 13536 seconds = 3 h 45 min 36 s |
Is 13536 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (13536 ÷ 2 = 6768) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (13536 ÷ 3 = 4512) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (13536 ÷ 4 = 3384) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | No (remainder 1) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (13536 ÷ 6 = 2256) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 5) | 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 | Yes (13536 ÷ 8 = 1692) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | Yes (13536 ÷ 9 = 1504) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | No (remainder 6) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 6) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (13536 ÷ 12 = 1128) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 13536 a prime number?
No. 13536 = × × 47, so it is divisible by 2.
What are the factors of 13536?
1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 32, 36, 47, 48, 72, 94, 96, 141, 144, 188, 282, 288, 376, 423, 564, 752, 846, 1128, 1504, 1692, 2256, 3384, 4512, 6768, 13536.
What is 13536 in binary?
11010011100000 (hexadecimal 34E0, octal 32340).
What is the square root of 13536?
About 116.3443, exactly 12√94.
Is 13536 divisible by 3?
Yes. Its digits add up to 18, a multiple of 3.
What is special about the number 13536?
13536 is a Harshad number: divisible by its digit sum 18.