The number 32016
32016 is a composite number with 40 divisors. Its prime factorisation is × 3 × 23 × 29. Divisors (40): 1, 2, 3, 4, 6, 8, 12, 16, 23, 24, 29, 46, 48, 58, 69, 87 … 32016.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 32016: a Harshad number: divisible by its digit sum 12.
- 2
32016 is composite. Its prime factorisation is
- 3
The divisors add up to 89280; without 32016 itself that is 57264, so 32016 is abundant (57264 is more than 32016). Euler's totient φ(32016) = 9856 numbers up to 32016 share no factor with it.
- 4
The digits of 32016 add up to 12, 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
\[ 32016 = 2^{4} \times 3 \times 23 \times 29 \]32016 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 40 |
| Sum of divisors | 89280 |
| Euler totient φ(n) | 9856 |
| Square | 1025024256 |
| Cube | 32817176580096 |
| Square root | 178.930154 (= 4√2001) |
| Digit sum / digital root | 12 / 3 |
| Collatz steps to 1 | 54 |
| Scientific notation | 3.2016 × |
32016 in other forms
| Form | Value |
|---|---|
| In words | thirty-two thousand and sixteen |
| Binary (base 2) | 111110100010000 |
| Octal (base 8) | 76420 |
| Hexadecimal (base 16) | 7D10 |
| Base 3 | 1121220210 |
| As time | 32016 seconds = 8 h 53 min 36 s |
Is 32016 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (32016 ÷ 2 = 16008) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (32016 ÷ 3 = 10672) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (32016 ÷ 4 = 8004) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | No (remainder 1) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (32016 ÷ 6 = 5336) | 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 (32016 ÷ 8 = 4002) | 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 6) | 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 (32016 ÷ 12 = 2668) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 32016 a prime number?
No. 32016 = × 3 × 23 × 29, so it is divisible by 2.
What are the factors of 32016?
1, 2, 3, 4, 6, 8, 12, 16, 23, 24, 29, 46, 48, 58, 69, 87, 92, 116, 138, 174, 184, 232, 276, 348, 368, 464, 552, 667, 696, 1104, 1334, 1392, 2001, 2668, 4002, 5336, 8004, 10672, 16008, 32016.
What is 32016 in binary?
111110100010000 (hexadecimal 7D10, octal 76420).
What is the square root of 32016?
About 178.9302, exactly 4√2001.
Is 32016 divisible by 3?
Yes. Its digits add up to 12, a multiple of 3.
What is special about the number 32016?
32016 is a Harshad number: divisible by its digit sum 12.