The number 32736
32736 is a composite number with 48 divisors. Its prime factorisation is × 3 × 11 × 31. Divisors (48): 1, 2, 3, 4, 6, 8, 11, 12, 16, 22, 24, 31, 32, 33, 44, 48 … 32736.
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How to work it out
- 1
32736 has no famous special property in the usual lists (prime, square, cube, triangular, Fibonacci, palindrome, perfect), but it is still a composite number.
- 2
32736 is composite. Its prime factorisation is
- 3
The divisors add up to 96768; without 32736 itself that is 64032, so 32736 is abundant (64032 is more than 32736). Euler's totient φ(32736) = 9600 numbers up to 32736 share no factor with it.
- 4
The digits of 32736 add up to 21, and repeating that until one digit is left gives the digital root 3. The Collatz sequence (halve if even, else 3n+1) takes 67 steps to reach 1.
LaTeX source of the formulas on this page
\[ 32736 = 2^{5} \times 3 \times 11 \times 31 \]32736 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 48 |
| Sum of divisors | 96768 |
| Euler totient φ(n) | 9600 |
| Square | 1071645696 |
| Cube | 35081393504256 |
| Square root | 180.930926 (= 4√2046) |
| Digit sum / digital root | 21 / 3 |
| Collatz steps to 1 | 67 |
| Scientific notation | 3.2736 × |
32736 in other forms
| Form | Value |
|---|---|
| In words | thirty-two thousand seven hundred and thirty-six |
| Binary (base 2) | 111111111100000 |
| Octal (base 8) | 77740 |
| Hexadecimal (base 16) | 7FE0 |
| Base 3 | 1122220110 |
| As time | 32736 seconds = 9 h 5 min 36 s |
Is 32736 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (32736 ÷ 2 = 16368) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (32736 ÷ 3 = 10912) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (32736 ÷ 4 = 8184) | 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 (32736 ÷ 6 = 5456) | 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 | Yes (32736 ÷ 8 = 4092) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 3) | 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 | Yes (32736 ÷ 11 = 2976) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (32736 ÷ 12 = 2728) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 32736 a prime number?
No. 32736 = × 3 × 11 × 31, so it is divisible by 2.
What are the factors of 32736?
1, 2, 3, 4, 6, 8, 11, 12, 16, 22, 24, 31, 32, 33, 44, 48, 62, 66, 88, 93, 96, 124, 132, 176, 186, 248, 264, 341, 352, 372, 496, 528, 682, 744, 992, 1023, 1056, 1364, 1488, 2046, 2728, 2976, 4092, 5456, 8184, 10912, 16368, 32736.
What is 32736 in binary?
111111111100000 (hexadecimal 7FE0, octal 77740).
What is the square root of 32736?
About 180.9309, exactly 4√2046.
Is 32736 divisible by 3?
Yes. Its digits add up to 21, a multiple of 3.
What is special about the number 32736?
It is a composite number with 48 divisors.