The number 80784
80784 is a composite number with 80 divisors. Its prime factorisation is × × 11 × 17. Divisors (80): 1, 2, 3, 4, 6, 8, 9, 11, 12, 16, 17, 18, 22, 24, 27, 33 … 80784.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 80784: a happy number: repeatedly adding the squares of its digits reaches 1; a Harshad number: divisible by its digit sum 27.
- 2
80784 is composite. Its prime factorisation is
- 3
The divisors add up to 267840; without 80784 itself that is 187056, so 80784 is abundant (187056 is more than 80784). Euler's totient φ(80784) = 23040 numbers up to 80784 share no factor with it.
- 4
The digits of 80784 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 89 steps to reach 1.
LaTeX source of the formulas on this page
\[ 80784 = 2^{4} \times 3^{3} \times 11 \times 17 \]80784 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 80 |
| Sum of divisors | 267840 |
| Euler totient φ(n) | 23040 |
| Square | 6526054656 |
| Cube | 527200799330304 |
| Square root | 284.225263 (= 12√561) |
| Digit sum / digital root | 27 / 9 |
| Collatz steps to 1 | 89 |
| Scientific notation | 8.0784 × |
80784 in other forms
| Form | Value |
|---|---|
| In words | eighty thousand seven hundred and eighty-four |
| Binary (base 2) | 10011101110010000 |
| Octal (base 8) | 235620 |
| Hexadecimal (base 16) | 13B90 |
| Base 3 | 11002211000 |
| As time | 80784 seconds = 22 h 26 min 24 s |
Is 80784 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (80784 ÷ 2 = 40392) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (80784 ÷ 3 = 26928) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (80784 ÷ 4 = 20196) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | No (remainder 4) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (80784 ÷ 6 = 13464) | 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 (80784 ÷ 8 = 10098) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | Yes (80784 ÷ 9 = 8976) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | No (remainder 4) | A number is divisible by 10 if the last digit is 0. |
| 11 | Yes (80784 ÷ 11 = 7344) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (80784 ÷ 12 = 6732) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 80784 a prime number?
No. 80784 = × × 11 × 17, so it is divisible by 2.
What are the factors of 80784?
1, 2, 3, 4, 6, 8, 9, 11, 12, 16, 17, 18, 22, 24, 27, 33, 34, 36, 44, 48, 51, 54, 66, 68, 72, 88, 99, 102, 108, 132, 136, 144, 153, 176, 187, 198, 204, 216, 264, 272, 297, 306, 374, 396, 408, 432, 459, 528, 561, 594, 612, 748, 792, 816, 918, 1122, 1188, 1224, 1496, 1584, 1683, 1836, 2244, 2376, 2448, 2992, 3366, 3672, 4488, 4752, 5049, 6732, 7344, 8976, 10098, 13464, 20196, 26928, 40392, 80784.
What is 80784 in binary?
10011101110010000 (hexadecimal 13B90, octal 235620).
What is the square root of 80784?
About 284.2253, exactly 12√561.
Is 80784 divisible by 3?
Yes. Its digits add up to 27, a multiple of 3.
What is special about the number 80784?
80784 is a happy number: repeatedly adding the squares of its digits reaches 1; a Harshad number: divisible by its digit sum 27.