The number 37728
37728 is a composite number with 36 divisors. Its prime factorisation is × × 131. Divisors (36): 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 32, 36, 48, 72, 96 … 37728.
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How to work it out
- 1
37728 has no famous special property in the usual lists (prime, square, cube, triangular, Fibonacci, palindrome, perfect), but it is still a composite number.
- 2
37728 is composite. Its prime factorisation is
- 3
The divisors add up to 108108; without 37728 itself that is 70380, so 37728 is abundant (70380 is more than 37728). Euler's totient φ(37728) = 12480 numbers up to 37728 share no factor with it.
- 4
The digits of 37728 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 62 steps to reach 1.
LaTeX source of the formulas on this page
\[ 37728 = 2^{5} \times 3^{2} \times 131 \]37728 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 36 |
| Sum of divisors | 108108 |
| Euler totient φ(n) | 12480 |
| Square | 1423401984 |
| Cube | 53702110052352 |
| Square root | 194.236969 (= 12√262) |
| Digit sum / digital root | 27 / 9 |
| Collatz steps to 1 | 62 |
| Scientific notation | 3.7728 × |
37728 in other forms
| Form | Value |
|---|---|
| In words | thirty-seven thousand seven hundred and twenty-eight |
| Binary (base 2) | 1001001101100000 |
| Octal (base 8) | 111540 |
| Hexadecimal (base 16) | 9360 |
| Base 3 | 1220202100 |
| As time | 37728 seconds = 10 h 28 min 48 s |
Is 37728 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (37728 ÷ 2 = 18864) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (37728 ÷ 3 = 12576) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (37728 ÷ 4 = 9432) | 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 (37728 ÷ 6 = 6288) | 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 (37728 ÷ 8 = 4716) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | Yes (37728 ÷ 9 = 4192) | 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 9) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (37728 ÷ 12 = 3144) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 37728 a prime number?
No. 37728 = × × 131, so it is divisible by 2.
What are the factors of 37728?
1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 32, 36, 48, 72, 96, 131, 144, 262, 288, 393, 524, 786, 1048, 1179, 1572, 2096, 2358, 3144, 4192, 4716, 6288, 9432, 12576, 18864, 37728.
What is 37728 in binary?
1001001101100000 (hexadecimal 9360, octal 111540).
What is the square root of 37728?
About 194.2370, exactly 12√262.
Is 37728 divisible by 3?
Yes. Its digits add up to 27, a multiple of 3.
What is special about the number 37728?
It is a composite number with 36 divisors.