The number 33408
33408 is a composite number with 48 divisors. Its prime factorisation is × × 29. Divisors (48): 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 29, 32, 36, 48, 58 … 33408.
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How to work it out
- 1
What is special about 33408: a Harshad number: divisible by its digit sum 18.
- 2
33408 is composite. Its prime factorisation is
- 3
The divisors add up to 99450; without 33408 itself that is 66042, so 33408 is abundant (66042 is more than 33408). Euler's totient φ(33408) = 10752 numbers up to 33408 share no factor with it.
- 4
The digits of 33408 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 36 steps to reach 1.
LaTeX source of the formulas on this page
\[ 33408 = 2^{7} \times 3^{2} \times 29 \]33408 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 48 |
| Sum of divisors | 99450 |
| Euler totient φ(n) | 10752 |
| Square | 1116094464 |
| Cube | 37286483853312 |
| Square root | 182.778555 (= 24√58) |
| Digit sum / digital root | 18 / 9 |
| Collatz steps to 1 | 36 |
| Scientific notation | 3.3408 × |
33408 in other forms
| Form | Value |
|---|---|
| In words | thirty-three thousand four hundred and eight |
| Binary (base 2) | 1000001010000000 |
| Octal (base 8) | 101200 |
| Hexadecimal (base 16) | 8280 |
| Base 3 | 1200211100 |
| As time | 33408 seconds = 9 h 16 min 48 s |
Is 33408 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (33408 ÷ 2 = 16704) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (33408 ÷ 3 = 11136) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (33408 ÷ 4 = 8352) | 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 (33408 ÷ 6 = 5568) | 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 (33408 ÷ 8 = 4176) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | Yes (33408 ÷ 9 = 3712) | 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 1) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (33408 ÷ 12 = 2784) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 33408 a prime number?
No. 33408 = × × 29, so it is divisible by 2.
What are the factors of 33408?
1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 29, 32, 36, 48, 58, 64, 72, 87, 96, 116, 128, 144, 174, 192, 232, 261, 288, 348, 384, 464, 522, 576, 696, 928, 1044, 1152, 1392, 1856, 2088, 2784, 3712, 4176, 5568, 8352, 11136, 16704, 33408.
What is 33408 in binary?
1000001010000000 (hexadecimal 8280, octal 101200).
What is the square root of 33408?
About 182.7786, exactly 24√58.
Is 33408 divisible by 3?
Yes. Its digits add up to 18, a multiple of 3.
What is special about the number 33408?
33408 is a Harshad number: divisible by its digit sum 18.