The number 33488
33488 is a composite number with 40 divisors. Its prime factorisation is × 7 × 13 × 23. Divisors (40): 1, 2, 4, 7, 8, 13, 14, 16, 23, 26, 28, 46, 52, 56, 91, 92 … 33488.
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How to work it out
- 1
What is special about 33488: a Harshad number: divisible by its digit sum 26.
- 2
33488 is composite. Its prime factorisation is
- 3
The divisors add up to 83328; without 33488 itself that is 49840, so 33488 is abundant (49840 is more than 33488). Euler's totient φ(33488) = 12672 numbers up to 33488 share no factor with it.
- 4
The digits of 33488 add up to 26, and repeating that until one digit is left gives the digital root 8. The Collatz sequence (halve if even, else 3n+1) takes 129 steps to reach 1.
LaTeX source of the formulas on this page
\[ 33488 = 2^{4} \times 7 \times 13 \times 23 \]33488 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 40 |
| Sum of divisors | 83328 |
| Euler totient φ(n) | 12672 |
| Square | 1121446144 |
| Cube | 37554988470272 |
| Square root | 182.997268 (= 4√2093) |
| Digit sum / digital root | 26 / 8 |
| Collatz steps to 1 | 129 |
| Scientific notation | 3.3488 × |
33488 in other forms
| Form | Value |
|---|---|
| In words | thirty-three thousand four hundred and eighty-eight |
| Binary (base 2) | 1000001011010000 |
| Octal (base 8) | 101320 |
| Hexadecimal (base 16) | 82D0 |
| Base 3 | 1200221022 |
| As time | 33488 seconds = 9 h 18 min 8 s |
Is 33488 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (33488 ÷ 2 = 16744) | 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 (33488 ÷ 4 = 8372) | 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 | Yes (33488 ÷ 7 = 4784) | 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 (33488 ÷ 8 = 4186) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 8) | 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 4) | 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 33488 a prime number?
No. 33488 = × 7 × 13 × 23, so it is divisible by 2.
What are the factors of 33488?
1, 2, 4, 7, 8, 13, 14, 16, 23, 26, 28, 46, 52, 56, 91, 92, 104, 112, 161, 182, 184, 208, 299, 322, 364, 368, 598, 644, 728, 1196, 1288, 1456, 2093, 2392, 2576, 4186, 4784, 8372, 16744, 33488.
What is 33488 in binary?
1000001011010000 (hexadecimal 82D0, octal 101320).
What is the square root of 33488?
About 182.9973, exactly 4√2093.
Is 33488 divisible by 3?
No. Its digits add up to 26, which is not a multiple of 3.
What is special about the number 33488?
33488 is a Harshad number: divisible by its digit sum 26.