The number 72816
72816 is a composite number with 40 divisors. Its prime factorisation is × 3 × 37 × 41. Divisors (40): 1, 2, 3, 4, 6, 8, 12, 16, 24, 37, 41, 48, 74, 82, 111, 123 … 72816.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 72816: a Harshad number: divisible by its digit sum 24.
- 2
72816 is composite. Its prime factorisation is
- 3
The divisors add up to 197904; without 72816 itself that is 125088, so 72816 is abundant (125088 is more than 72816). Euler's totient φ(72816) = 23040 numbers up to 72816 share no factor with it.
- 4
The digits of 72816 add up to 24, and repeating that until one digit is left gives the digital root 6. The Collatz sequence (halve if even, else 3n+1) takes 187 steps to reach 1.
LaTeX source of the formulas on this page
\[ 72816 = 2^{4} \times 3 \times 37 \times 41 \]72816 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 40 |
| Sum of divisors | 197904 |
| Euler totient φ(n) | 23040 |
| Square | 5302169856 |
| Cube | 386082800234496 |
| Square root | 269.844400 (= 4√4551) |
| Digit sum / digital root | 24 / 6 |
| Collatz steps to 1 | 187 |
| Scientific notation | 7.2816 × |
72816 in other forms
| Form | Value |
|---|---|
| In words | seventy-two thousand eight hundred and sixteen |
| Binary (base 2) | 10001110001110000 |
| Octal (base 8) | 216160 |
| Hexadecimal (base 16) | 11C70 |
| Base 3 | 10200212220 |
| As time | 72816 seconds = 20 h 13 min 36 s |
Is 72816 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (72816 ÷ 2 = 36408) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (72816 ÷ 3 = 24272) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (72816 ÷ 4 = 18204) | 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 (72816 ÷ 6 = 12136) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 2) | 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 (72816 ÷ 8 = 9102) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 6) | 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 7) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (72816 ÷ 12 = 6068) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 72816 a prime number?
No. 72816 = × 3 × 37 × 41, so it is divisible by 2.
What are the factors of 72816?
1, 2, 3, 4, 6, 8, 12, 16, 24, 37, 41, 48, 74, 82, 111, 123, 148, 164, 222, 246, 296, 328, 444, 492, 592, 656, 888, 984, 1517, 1776, 1968, 3034, 4551, 6068, 9102, 12136, 18204, 24272, 36408, 72816.
What is 72816 in binary?
10001110001110000 (hexadecimal 11C70, octal 216160).
What is the square root of 72816?
About 269.8444, exactly 4√4551.
Is 72816 divisible by 3?
Yes. Its digits add up to 24, a multiple of 3.
What is special about the number 72816?
72816 is a Harshad number: divisible by its digit sum 24.