The number 33345
33345 is a binary palindrome (1000001001000001). Its prime factorisation is × 5 × 13 × 19. Divisors (32): 1, 3, 5, 9, 13, 15, 19, 27, 39, 45, 57, 65, 95, 117, 135, 171 … 33345.
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How to work it out
- 1
What is special about 33345: a binary palindrome (1000001001000001); a happy number: repeatedly adding the squares of its digits reaches 1.
- 2
33345 is composite. Its prime factorisation is
- 3
The divisors add up to 67200; without 33345 itself that is 33855, so 33345 is abundant (33855 is more than 33345). Euler's totient φ(33345) = 15552 numbers up to 33345 share no factor with it.
- 4
The digits of 33345 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 160 steps to reach 1.
LaTeX source of the formulas on this page
\[ 33345 = 3^{3} \times 5 \times 13 \times 19 \]33345 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 32 |
| Sum of divisors | 67200 |
| Euler totient φ(n) | 15552 |
| Square | 1111889025 |
| Cube | 37075939538625 |
| Square root | 182.606134 (= 3√3705) |
| Digit sum / digital root | 18 / 9 |
| Collatz steps to 1 | 160 |
| Scientific notation | 3.3345 × |
33345 in other forms
| Form | Value |
|---|---|
| In words | thirty-three thousand three hundred and forty-five |
| Binary (base 2) | 1000001001000001 |
| Octal (base 8) | 101101 |
| Hexadecimal (base 16) | 8241 |
| Base 3 | 1200202000 |
| As time | 33345 seconds = 9 h 15 min 45 s |
Is 33345 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | No (remainder 1) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (33345 ÷ 3 = 11115) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | No (remainder 1) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | Yes (33345 ÷ 5 = 6669) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | No (remainder 3) | 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 | No (remainder 1) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | Yes (33345 ÷ 9 = 3705) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | No (remainder 5) | 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 9) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 33345 a prime number?
No. 33345 = × 5 × 13 × 19, so it is divisible by 3.
What are the factors of 33345?
1, 3, 5, 9, 13, 15, 19, 27, 39, 45, 57, 65, 95, 117, 135, 171, 195, 247, 285, 351, 513, 585, 741, 855, 1235, 1755, 2223, 2565, 3705, 6669, 11115, 33345.
What is 33345 in binary?
1000001001000001 (hexadecimal 8241, octal 101101).
What is the square root of 33345?
About 182.6061, exactly 3√3705.
Is 33345 divisible by 3?
Yes. Its digits add up to 18, a multiple of 3.
What is special about the number 33345?
33345 is a binary palindrome (1000001001000001); a happy number: repeatedly adding the squares of its digits reaches 1.