The number 33072
33072 is a composite number with 40 divisors. Its prime factorisation is × 3 × 13 × 53. Divisors (40): 1, 2, 3, 4, 6, 8, 12, 13, 16, 24, 26, 39, 48, 52, 53, 78 … 33072.
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How to work it out
- 1
33072 has no famous special property in the usual lists (prime, square, cube, triangular, Fibonacci, palindrome, perfect), but it is still a composite number.
- 2
33072 is composite. Its prime factorisation is
- 3
The divisors add up to 93744; without 33072 itself that is 60672, so 33072 is abundant (60672 is more than 33072). Euler's totient φ(33072) = 9984 numbers up to 33072 share no factor with it.
- 4
The digits of 33072 add up to 15, and repeating that until one digit is left gives the digital root 6. The Collatz sequence (halve if even, else 3n+1) takes 160 steps to reach 1.
LaTeX source of the formulas on this page
\[ 33072 = 2^{4} \times 3 \times 13 \times 53 \]33072 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 40 |
| Sum of divisors | 93744 |
| Euler totient φ(n) | 9984 |
| Square | 1093757184 |
| Cube | 36172737589248 |
| Square root | 181.857087 (= 4√2067) |
| Digit sum / digital root | 15 / 6 |
| Collatz steps to 1 | 160 |
| Scientific notation | 3.3072 × |
33072 in other forms
| Form | Value |
|---|---|
| In words | thirty-three thousand and seventy-two |
| Binary (base 2) | 1000000100110000 |
| Octal (base 8) | 100460 |
| Hexadecimal (base 16) | 8130 |
| Base 3 | 1200100220 |
| As time | 33072 seconds = 9 h 11 min 12 s |
Is 33072 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (33072 ÷ 2 = 16536) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (33072 ÷ 3 = 11024) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (33072 ÷ 4 = 8268) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | No (remainder 2) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (33072 ÷ 6 = 5512) | 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 | Yes (33072 ÷ 8 = 4134) | 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 2) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 6) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (33072 ÷ 12 = 2756) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 33072 a prime number?
No. 33072 = × 3 × 13 × 53, so it is divisible by 2.
What are the factors of 33072?
1, 2, 3, 4, 6, 8, 12, 13, 16, 24, 26, 39, 48, 52, 53, 78, 104, 106, 156, 159, 208, 212, 312, 318, 424, 624, 636, 689, 848, 1272, 1378, 2067, 2544, 2756, 4134, 5512, 8268, 11024, 16536, 33072.
What is 33072 in binary?
1000000100110000 (hexadecimal 8130, octal 100460).
What is the square root of 33072?
About 181.8571, exactly 4√2067.
Is 33072 divisible by 3?
Yes. Its digits add up to 15, a multiple of 3.
What is special about the number 33072?
It is a composite number with 40 divisors.