The number 33648
33648 is a composite number with 20 divisors. Its prime factorisation is × 3 × 701. Divisors (20): 1, 2, 3, 4, 6, 8, 12, 16, 24, 48, 701, 1402, 2103, 2804, 4206, 5608 … 33648.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 33648: a Harshad number: divisible by its digit sum 24.
- 2
33648 is composite. Its prime factorisation is
- 3
The divisors add up to 87048; without 33648 itself that is 53400, so 33648 is abundant (53400 is more than 33648). Euler's totient φ(33648) = 11200 numbers up to 33648 share no factor with it.
- 4
The digits of 33648 add up to 24, and repeating that until one digit is left gives the digital root 6. The Collatz sequence (halve if even, else 3n+1) takes 98 steps to reach 1.
LaTeX source of the formulas on this page
\[ 33648 = 2^{4} \times 3 \times 701 \]33648 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 20 |
| Sum of divisors | 87048 |
| Euler totient φ(n) | 11200 |
| Square | 1132187904 |
| Cube | 38095858593792 |
| Square root | 183.433912 (= 4√2103) |
| Digit sum / digital root | 24 / 6 |
| Collatz steps to 1 | 98 |
| Scientific notation | 3.3648 × |
33648 in other forms
| Form | Value |
|---|---|
| In words | thirty-three thousand six hundred and forty-eight |
| Binary (base 2) | 1000001101110000 |
| Octal (base 8) | 101560 |
| Hexadecimal (base 16) | 8370 |
| Base 3 | 1201011020 |
| As time | 33648 seconds = 9 h 20 min 48 s |
Is 33648 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (33648 ÷ 2 = 16824) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (33648 ÷ 3 = 11216) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (33648 ÷ 4 = 8412) | 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 (33648 ÷ 6 = 5608) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 6) | 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 (33648 ÷ 8 = 4206) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 6) | 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 10) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (33648 ÷ 12 = 2804) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 33648 a prime number?
No. 33648 = × 3 × 701, so it is divisible by 2.
What are the factors of 33648?
1, 2, 3, 4, 6, 8, 12, 16, 24, 48, 701, 1402, 2103, 2804, 4206, 5608, 8412, 11216, 16824, 33648.
What is 33648 in binary?
1000001101110000 (hexadecimal 8370, octal 101560).
What is the square root of 33648?
About 183.4339, exactly 4√2103.
Is 33648 divisible by 3?
Yes. Its digits add up to 24, a multiple of 3.
What is special about the number 33648?
33648 is a Harshad number: divisible by its digit sum 24.