The number 33728
33728 is a composite number with 28 divisors. Its prime factorisation is × 17 × 31. Divisors (28): 1, 2, 4, 8, 16, 17, 31, 32, 34, 62, 64, 68, 124, 136, 248, 272 … 33728.
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How to work it out
- 1
33728 has no famous special property in the usual lists (prime, square, cube, triangular, Fibonacci, palindrome, perfect), but it is still a composite number.
- 2
33728 is composite. Its prime factorisation is
- 3
The divisors add up to 73152; without 33728 itself that is 39424, so 33728 is abundant (39424 is more than 33728). Euler's totient φ(33728) = 15360 numbers up to 33728 share no factor with it.
- 4
The digits of 33728 add up to 23, and repeating that until one digit is left gives the digital root 5. The Collatz sequence (halve if even, else 3n+1) takes 85 steps to reach 1.
LaTeX source of the formulas on this page
\[ 33728 = 2^{6} \times 17 \times 31 \]33728 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 28 |
| Sum of divisors | 73152 |
| Euler totient φ(n) | 15360 |
| Square | 1137577984 |
| Cube | 38368230244352 |
| Square root | 183.651845 (= 8√527) |
| Digit sum / digital root | 23 / 5 |
| Collatz steps to 1 | 85 |
| Scientific notation | 3.3728 × |
33728 in other forms
| Form | Value |
|---|---|
| In words | thirty-three thousand seven hundred and twenty-eight |
| Binary (base 2) | 1000001111000000 |
| Octal (base 8) | 101700 |
| Hexadecimal (base 16) | 83C0 |
| Base 3 | 1201021012 |
| As time | 33728 seconds = 9 h 22 min 8 s |
Is 33728 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (33728 ÷ 2 = 16864) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | No (remainder 2) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (33728 ÷ 4 = 8432) | 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 2) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 2) | 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 (33728 ÷ 8 = 4216) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 5) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | No (remainder 8) | 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 | No (remainder 8) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 33728 a prime number?
No. 33728 = × 17 × 31, so it is divisible by 2.
What are the factors of 33728?
1, 2, 4, 8, 16, 17, 31, 32, 34, 62, 64, 68, 124, 136, 248, 272, 496, 527, 544, 992, 1054, 1088, 1984, 2108, 4216, 8432, 16864, 33728.
What is 33728 in binary?
1000001111000000 (hexadecimal 83C0, octal 101700).
What is the square root of 33728?
About 183.6518, exactly 8√527.
Is 33728 divisible by 3?
No. Its digits add up to 23, which is not a multiple of 3.
What is special about the number 33728?
It is a composite number with 28 divisors.