The number 72016
72016 is a composite number with 20 divisors. Its prime factorisation is × 7 × 643. Divisors (20): 1, 2, 4, 7, 8, 14, 16, 28, 56, 112, 643, 1286, 2572, 4501, 5144, 9002 … 72016.
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How to work it out
- 1
What is special about 72016: a Harshad number: divisible by its digit sum 16.
- 2
72016 is composite. Its prime factorisation is
- 3
The divisors add up to 159712; without 72016 itself that is 87696, so 72016 is abundant (87696 is more than 72016). Euler's totient φ(72016) = 30816 numbers up to 72016 share no factor with it.
- 4
The digits of 72016 add up to 16, and repeating that until one digit is left gives the digital root 7. The Collatz sequence (halve if even, else 3n+1) takes 50 steps to reach 1.
LaTeX source of the formulas on this page
\[ 72016 = 2^{4} \times 7 \times 643 \]72016 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 20 |
| Sum of divisors | 159712 |
| Euler totient φ(n) | 30816 |
| Square | 5186304256 |
| Cube | 373496887300096 |
| Square root | 268.357970 (= 4√4501) |
| Digit sum / digital root | 16 / 7 |
| Collatz steps to 1 | 50 |
| Scientific notation | 7.2016 × |
72016 in other forms
| Form | Value |
|---|---|
| In words | seventy-two thousand and sixteen |
| Binary (base 2) | 10001100101010000 |
| Octal (base 8) | 214520 |
| Hexadecimal (base 16) | 11950 |
| Base 3 | 10122210021 |
| As time | 72016 seconds = 20 h 0 min 16 s |
Is 72016 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (72016 ÷ 2 = 36008) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | No (remainder 1) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (72016 ÷ 4 = 18004) | 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 | No (remainder 4) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | Yes (72016 ÷ 7 = 10288) | 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 (72016 ÷ 8 = 9002) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 7) | 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 10) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | No (remainder 4) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 72016 a prime number?
No. 72016 = × 7 × 643, so it is divisible by 2.
What are the factors of 72016?
1, 2, 4, 7, 8, 14, 16, 28, 56, 112, 643, 1286, 2572, 4501, 5144, 9002, 10288, 18004, 36008, 72016.
What is 72016 in binary?
10001100101010000 (hexadecimal 11950, octal 214520).
What is the square root of 72016?
About 268.3580, exactly 4√4501.
Is 72016 divisible by 3?
No. Its digits add up to 16, which is not a multiple of 3.
What is special about the number 72016?
72016 is a Harshad number: divisible by its digit sum 16.