The number 33678
33678 is a composite number with 12 divisors. Its prime factorisation is 2 × × 1871. Divisors (12): 1, 2, 3, 6, 9, 18, 1871, 3742, 5613, 11226, 16839, 33678.
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How to work it out
- 1
What is special about 33678: a happy number: repeatedly adding the squares of its digits reaches 1.
- 2
33678 is composite. Its prime factorisation is
- 3
The divisors add up to 73008; without 33678 itself that is 39330, so 33678 is abundant (39330 is more than 33678). Euler's totient φ(33678) = 11220 numbers up to 33678 share no factor with it.
- 4
The digits of 33678 add up to 27, and repeating that until one digit is left gives the digital root 9. The Collatz sequence (halve if even, else 3n+1) takes 67 steps to reach 1.
LaTeX source of the formulas on this page
\[ 33678 = 2 \times 3^{2} \times 1871 \]33678 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 12 |
| Sum of divisors | 73008 |
| Euler totient φ(n) | 11220 |
| Square | 1134207684 |
| Cube | 38197846381752 |
| Square root | 183.515667 (= 3√3742) |
| Digit sum / digital root | 27 / 9 |
| Collatz steps to 1 | 67 |
| Scientific notation | 3.3678 × |
33678 in other forms
| Form | Value |
|---|---|
| In words | thirty-three thousand six hundred and seventy-eight |
| Binary (base 2) | 1000001110001110 |
| Octal (base 8) | 101616 |
| Hexadecimal (base 16) | 838E |
| Base 3 | 1201012100 |
| As time | 33678 seconds = 9 h 21 min 18 s |
Is 33678 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (33678 ÷ 2 = 16839) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (33678 ÷ 3 = 11226) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | No (remainder 2) | 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 (33678 ÷ 6 = 5613) | 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 | No (remainder 6) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | Yes (33678 ÷ 9 = 3742) | 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 7) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | No (remainder 6) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 33678 a prime number?
No. 33678 = 2 × × 1871, so it is divisible by 2.
What are the factors of 33678?
1, 2, 3, 6, 9, 18, 1871, 3742, 5613, 11226, 16839, 33678.
What is 33678 in binary?
1000001110001110 (hexadecimal 838E, octal 101616).
What is the square root of 33678?
About 183.5157, exactly 3√3742.
Is 33678 divisible by 3?
Yes. Its digits add up to 27, a multiple of 3.
What is special about the number 33678?
33678 is a happy number: repeatedly adding the squares of its digits reaches 1.