The number 33664
33664 is a composite number with 16 divisors. Its prime factorisation is × 263. Divisors (16): 1, 2, 4, 8, 16, 32, 64, 128, 263, 526, 1052, 2104, 4208, 8416, 16832, 33664.
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How to work it out
- 1
33664 has no famous special property in the usual lists (prime, square, cube, triangular, Fibonacci, palindrome, perfect), but it is still a composite number.
- 2
33664 is composite. Its prime factorisation is
- 3
The divisors add up to 67320; without 33664 itself that is 33656, so 33664 is deficient (33656 is less than 33664). Euler's totient φ(33664) = 16768 numbers up to 33664 share no factor with it.
- 4
The digits of 33664 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 85 steps to reach 1.
LaTeX source of the formulas on this page
\[ 33664 = 2^{7} \times 263 \]33664 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 16 |
| Sum of divisors | 67320 |
| Euler totient φ(n) | 16768 |
| Square | 1133264896 |
| Cube | 38150229458944 |
| Square root | 183.477519 (= 8√526) |
| Digit sum / digital root | 22 / 4 |
| Collatz steps to 1 | 85 |
| Scientific notation | 3.3664 × |
33664 in other forms
| Form | Value |
|---|---|
| In words | thirty-three thousand six hundred and sixty-four |
| Binary (base 2) | 1000001110000000 |
| Octal (base 8) | 101600 |
| Hexadecimal (base 16) | 8380 |
| Base 3 | 1201011211 |
| As time | 33664 seconds = 9 h 21 min 4 s |
Is 33664 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (33664 ÷ 2 = 16832) | 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 (33664 ÷ 4 = 8416) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | No (remainder 4) | 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 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 (33664 ÷ 8 = 4208) | 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 4) | 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 4) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 33664 a prime number?
No. 33664 = × 263, so it is divisible by 2.
What are the factors of 33664?
1, 2, 4, 8, 16, 32, 64, 128, 263, 526, 1052, 2104, 4208, 8416, 16832, 33664.
What is 33664 in binary?
1000001110000000 (hexadecimal 8380, octal 101600).
What is the square root of 33664?
About 183.4775, exactly 8√526.
Is 33664 divisible by 3?
No. Its digits add up to 22, which is not a multiple of 3.
What is special about the number 33664?
It is a composite number with 16 divisors.