The number 33680
33680 is a composite number with 20 divisors. Its prime factorisation is × 5 × 421. Divisors (20): 1, 2, 4, 5, 8, 10, 16, 20, 40, 80, 421, 842, 1684, 2105, 3368, 4210 … 33680.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 33680: a Harshad number: divisible by its digit sum 20.
- 2
33680 is composite. Its prime factorisation is
- 3
The divisors add up to 78492; without 33680 itself that is 44812, so 33680 is abundant (44812 is more than 33680). Euler's totient φ(33680) = 13440 numbers up to 33680 share no factor with it.
- 4
The digits of 33680 add up to 20, and repeating that until one digit is left gives the digital root 2. The Collatz sequence (halve if even, else 3n+1) takes 129 steps to reach 1.
LaTeX source of the formulas on this page
\[ 33680 = 2^{4} \times 5 \times 421 \]33680 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 20 |
| Sum of divisors | 78492 |
| Euler totient φ(n) | 13440 |
| Square | 1134342400 |
| Cube | 38204652032000 |
| Square root | 183.521116 (= 4√2105) |
| Digit sum / digital root | 20 / 2 |
| Collatz steps to 1 | 129 |
| Scientific notation | 3.368 × |
33680 in other forms
| Form | Value |
|---|---|
| In words | thirty-three thousand six hundred and eighty |
| Binary (base 2) | 1000001110010000 |
| Octal (base 8) | 101620 |
| Hexadecimal (base 16) | 8390 |
| Base 3 | 1201012102 |
| As time | 33680 seconds = 9 h 21 min 20 s |
Is 33680 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (33680 ÷ 2 = 16840) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | No (remainder 2) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (33680 ÷ 4 = 8420) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | Yes (33680 ÷ 5 = 6736) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | No (remainder 2) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 3) | 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 (33680 ÷ 8 = 4210) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 2) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | Yes (33680 ÷ 10 = 3368) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 9) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | No (remainder 8) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 33680 a prime number?
No. 33680 = × 5 × 421, so it is divisible by 2.
What are the factors of 33680?
1, 2, 4, 5, 8, 10, 16, 20, 40, 80, 421, 842, 1684, 2105, 3368, 4210, 6736, 8420, 16840, 33680.
What is 33680 in binary?
1000001110010000 (hexadecimal 8390, octal 101620).
What is the square root of 33680?
About 183.5211, exactly 4√2105.
Is 33680 divisible by 3?
No. Its digits add up to 20, which is not a multiple of 3.
What is special about the number 33680?
33680 is a Harshad number: divisible by its digit sum 20.