The number 33948
33948 is a composite number with 36 divisors. Its prime factorisation is × × 23 × 41. Divisors (36): 1, 2, 3, 4, 6, 9, 12, 18, 23, 36, 41, 46, 69, 82, 92, 123 … 33948.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
33948 has no famous special property in the usual lists (prime, square, cube, triangular, Fibonacci, palindrome, perfect), but it is still a composite number.
- 2
33948 is composite. Its prime factorisation is
- 3
The divisors add up to 91728; without 33948 itself that is 57780, so 33948 is abundant (57780 is more than 33948). Euler's totient φ(33948) = 10560 numbers up to 33948 share no factor with it.
- 4
The digits of 33948 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 142 steps to reach 1.
LaTeX source of the formulas on this page
\[ 33948 = 2^{2} \times 3^{2} \times 23 \times 41 \]33948 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 36 |
| Sum of divisors | 91728 |
| Euler totient φ(n) | 10560 |
| Square | 1152466704 |
| Cube | 39123939667392 |
| Square root | 184.249830 (= 6√943) |
| Digit sum / digital root | 27 / 9 |
| Collatz steps to 1 | 142 |
| Scientific notation | 3.3948 × |
33948 in other forms
| Form | Value |
|---|---|
| In words | thirty-three thousand nine hundred and forty-eight |
| Binary (base 2) | 1000010010011100 |
| Octal (base 8) | 102234 |
| Hexadecimal (base 16) | 849C |
| Base 3 | 1201120100 |
| As time | 33948 seconds = 9 h 25 min 48 s |
Is 33948 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (33948 ÷ 2 = 16974) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (33948 ÷ 3 = 11316) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (33948 ÷ 4 = 8487) | 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 (33948 ÷ 6 = 5658) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 5) | 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 4) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | Yes (33948 ÷ 9 = 3772) | 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 2) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (33948 ÷ 12 = 2829) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 33948 a prime number?
No. 33948 = × × 23 × 41, so it is divisible by 2.
What are the factors of 33948?
1, 2, 3, 4, 6, 9, 12, 18, 23, 36, 41, 46, 69, 82, 92, 123, 138, 164, 207, 246, 276, 369, 414, 492, 738, 828, 943, 1476, 1886, 2829, 3772, 5658, 8487, 11316, 16974, 33948.
What is 33948 in binary?
1000010010011100 (hexadecimal 849C, octal 102234).
What is the square root of 33948?
About 184.2498, exactly 6√943.
Is 33948 divisible by 3?
Yes. Its digits add up to 27, a multiple of 3.
What is special about the number 33948?
It is a composite number with 36 divisors.