The number 33088
33088 is a composite number with 28 divisors. Its prime factorisation is × 11 × 47. Divisors (28): 1, 2, 4, 8, 11, 16, 22, 32, 44, 47, 64, 88, 94, 176, 188, 352 … 33088.
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How to work it out
- 1
What is special about 33088: a Harshad number: divisible by its digit sum 22.
- 2
33088 is composite. Its prime factorisation is
- 3
The divisors add up to 73152; without 33088 itself that is 40064, so 33088 is abundant (40064 is more than 33088). Euler's totient φ(33088) = 14720 numbers up to 33088 share no factor with it.
- 4
The digits of 33088 add up to 22, and repeating that until one digit is left gives the digital root 4. The Collatz sequence (halve if even, else 3n+1) takes 129 steps to reach 1.
LaTeX source of the formulas on this page
\[ 33088 = 2^{6} \times 11 \times 47 \]33088 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 28 |
| Sum of divisors | 73152 |
| Euler totient φ(n) | 14720 |
| Square | 1094815744 |
| Cube | 36225263337472 |
| Square root | 181.901072 (= 8√517) |
| Digit sum / digital root | 22 / 4 |
| Collatz steps to 1 | 129 |
| Scientific notation | 3.3088 × |
33088 in other forms
| Form | Value |
|---|---|
| In words | thirty-three thousand and eighty-eight |
| Binary (base 2) | 1000000101000000 |
| Octal (base 8) | 100500 |
| Hexadecimal (base 16) | 8140 |
| Base 3 | 1200101111 |
| As time | 33088 seconds = 9 h 11 min 28 s |
Is 33088 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (33088 ÷ 2 = 16544) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | No (remainder 1) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (33088 ÷ 4 = 8272) | 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 4) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 6) | 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 (33088 ÷ 8 = 4136) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 4) | 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 | Yes (33088 ÷ 11 = 3008) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | No (remainder 4) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 33088 a prime number?
No. 33088 = × 11 × 47, so it is divisible by 2.
What are the factors of 33088?
1, 2, 4, 8, 11, 16, 22, 32, 44, 47, 64, 88, 94, 176, 188, 352, 376, 517, 704, 752, 1034, 1504, 2068, 3008, 4136, 8272, 16544, 33088.
What is 33088 in binary?
1000000101000000 (hexadecimal 8140, octal 100500).
What is the square root of 33088?
About 181.9011, exactly 8√517.
Is 33088 divisible by 3?
No. Its digits add up to 22, which is not a multiple of 3.
What is special about the number 33088?
33088 is a Harshad number: divisible by its digit sum 22.