The number 33048
33048 is a composite number with 48 divisors. Its prime factorisation is × × 17. Divisors (48): 1, 2, 3, 4, 6, 8, 9, 12, 17, 18, 24, 27, 34, 36, 51, 54 … 33048.
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How to work it out
- 1
What is special about 33048: a Harshad number: divisible by its digit sum 18.
- 2
33048 is composite. Its prime factorisation is
- 3
The divisors add up to 98280; without 33048 itself that is 65232, so 33048 is abundant (65232 is more than 33048). Euler's totient φ(33048) = 10368 numbers up to 33048 share no factor with it.
- 4
The digits of 33048 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 129 steps to reach 1.
LaTeX source of the formulas on this page
\[ 33048 = 2^{3} \times 3^{5} \times 17 \]33048 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 48 |
| Sum of divisors | 98280 |
| Euler totient φ(n) | 10368 |
| Square | 1092170304 |
| Cube | 36094044206592 |
| Square root | 181.791089 (= 18√102) |
| Digit sum / digital root | 18 / 9 |
| Collatz steps to 1 | 129 |
| Scientific notation | 3.3048 × |
33048 in other forms
| Form | Value |
|---|---|
| In words | thirty-three thousand and forty-eight |
| Binary (base 2) | 1000000100011000 |
| Octal (base 8) | 100430 |
| Hexadecimal (base 16) | 8118 |
| Base 3 | 1200100000 |
| As time | 33048 seconds = 9 h 10 min 48 s |
Is 33048 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (33048 ÷ 2 = 16524) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (33048 ÷ 3 = 11016) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (33048 ÷ 4 = 8262) | 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 | Yes (33048 ÷ 6 = 5508) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 1) | 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 (33048 ÷ 8 = 4131) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | Yes (33048 ÷ 9 = 3672) | 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 | Yes (33048 ÷ 12 = 2754) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 33048 a prime number?
No. 33048 = × × 17, so it is divisible by 2.
What are the factors of 33048?
1, 2, 3, 4, 6, 8, 9, 12, 17, 18, 24, 27, 34, 36, 51, 54, 68, 72, 81, 102, 108, 136, 153, 162, 204, 216, 243, 306, 324, 408, 459, 486, 612, 648, 918, 972, 1224, 1377, 1836, 1944, 2754, 3672, 4131, 5508, 8262, 11016, 16524, 33048.
What is 33048 in binary?
1000000100011000 (hexadecimal 8118, octal 100430).
What is the square root of 33048?
About 181.7911, exactly 18√102.
Is 33048 divisible by 3?
Yes. Its digits add up to 18, a multiple of 3.
What is special about the number 33048?
33048 is a Harshad number: divisible by its digit sum 18.