The number 39072
39072 is a composite number with 48 divisors. Its prime factorisation is × 3 × 11 × 37. Divisors (48): 1, 2, 3, 4, 6, 8, 11, 12, 16, 22, 24, 32, 33, 37, 44, 48 … 39072.
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How to work it out
- 1
39072 has no famous special property in the usual lists (prime, square, cube, triangular, Fibonacci, palindrome, perfect), but it is still a composite number.
- 2
39072 is composite. Its prime factorisation is
- 3
The divisors add up to 114912; without 39072 itself that is 75840, so 39072 is abundant (75840 is more than 39072). Euler's totient φ(39072) = 11520 numbers up to 39072 share no factor with it.
- 4
The digits of 39072 add up to 21, and repeating that until one digit is left gives the digital root 3. The Collatz sequence (halve if even, else 3n+1) takes 44 steps to reach 1.
LaTeX source of the formulas on this page
\[ 39072 = 2^{5} \times 3 \times 11 \times 37 \]39072 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 48 |
| Sum of divisors | 114912 |
| Euler totient φ(n) | 11520 |
| Square | 1526621184 |
| Cube | 59648142901248 |
| Square root | 197.666386 (= 4√2442) |
| Digit sum / digital root | 21 / 3 |
| Collatz steps to 1 | 44 |
| Scientific notation | 3.9072 × |
39072 in other forms
| Form | Value |
|---|---|
| In words | thirty-nine thousand and seventy-two |
| Binary (base 2) | 1001100010100000 |
| Octal (base 8) | 114240 |
| Hexadecimal (base 16) | 98A0 |
| Base 3 | 1222121010 |
| As time | 39072 seconds = 10 h 51 min 12 s |
Is 39072 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (39072 ÷ 2 = 19536) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (39072 ÷ 3 = 13024) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (39072 ÷ 4 = 9768) | 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 (39072 ÷ 6 = 6512) | 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 | Yes (39072 ÷ 8 = 4884) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 3) | 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 | Yes (39072 ÷ 11 = 3552) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (39072 ÷ 12 = 3256) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 39072 a prime number?
No. 39072 = × 3 × 11 × 37, so it is divisible by 2.
What are the factors of 39072?
1, 2, 3, 4, 6, 8, 11, 12, 16, 22, 24, 32, 33, 37, 44, 48, 66, 74, 88, 96, 111, 132, 148, 176, 222, 264, 296, 352, 407, 444, 528, 592, 814, 888, 1056, 1184, 1221, 1628, 1776, 2442, 3256, 3552, 4884, 6512, 9768, 13024, 19536, 39072.
What is 39072 in binary?
1001100010100000 (hexadecimal 98A0, octal 114240).
What is the square root of 39072?
About 197.6664, exactly 4√2442.
Is 39072 divisible by 3?
Yes. Its digits add up to 21, a multiple of 3.
What is special about the number 39072?
It is a composite number with 48 divisors.