The number 31728
31728 is a composite number with 20 divisors. Its prime factorisation is × 3 × 661. Divisors (20): 1, 2, 3, 4, 6, 8, 12, 16, 24, 48, 661, 1322, 1983, 2644, 3966, 5288 … 31728.
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How to work it out
- 1
31728 has no famous special property in the usual lists (prime, square, cube, triangular, Fibonacci, palindrome, perfect), but it is still a composite number.
- 2
31728 is composite. Its prime factorisation is
- 3
The divisors add up to 82088; without 31728 itself that is 50360, so 31728 is abundant (50360 is more than 31728). Euler's totient φ(31728) = 10560 numbers up to 31728 share no factor with it.
- 4
The digits of 31728 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 54 steps to reach 1.
LaTeX source of the formulas on this page
\[ 31728 = 2^{4} \times 3 \times 661 \]31728 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 20 |
| Sum of divisors | 82088 |
| Euler totient φ(n) | 10560 |
| Square | 1006665984 |
| Cube | 31939498340352 |
| Square root | 178.123553 (= 4√1983) |
| Digit sum / digital root | 21 / 3 |
| Collatz steps to 1 | 54 |
| Scientific notation | 3.1728 × |
31728 in other forms
| Form | Value |
|---|---|
| In words | thirty-one thousand seven hundred and twenty-eight |
| Binary (base 2) | 111101111110000 |
| Octal (base 8) | 75760 |
| Hexadecimal (base 16) | 7BF0 |
| Base 3 | 1121112010 |
| As time | 31728 seconds = 8 h 48 min 48 s |
Is 31728 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (31728 ÷ 2 = 15864) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (31728 ÷ 3 = 10576) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (31728 ÷ 4 = 7932) | 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 (31728 ÷ 6 = 5288) | 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 (31728 ÷ 8 = 3966) | 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 8) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 4) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (31728 ÷ 12 = 2644) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 31728 a prime number?
No. 31728 = × 3 × 661, so it is divisible by 2.
What are the factors of 31728?
1, 2, 3, 4, 6, 8, 12, 16, 24, 48, 661, 1322, 1983, 2644, 3966, 5288, 7932, 10576, 15864, 31728.
What is 31728 in binary?
111101111110000 (hexadecimal 7BF0, octal 75760).
What is the square root of 31728?
About 178.1236, exactly 4√1983.
Is 31728 divisible by 3?
Yes. Its digits add up to 21, a multiple of 3.
What is special about the number 31728?
It is a composite number with 20 divisors.