The number 77824
77824 is a composite number with 26 divisors. Its prime factorisation is × 19. Divisors (26): 1, 2, 4, 8, 16, 19, 32, 38, 64, 76, 128, 152, 256, 304, 512, 608 … 77824.
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How to work it out
- 1
77824 has no famous special property in the usual lists (prime, square, cube, triangular, Fibonacci, palindrome, perfect), but it is still a composite number.
- 2
77824 is composite. Its prime factorisation is
- 3
The divisors add up to 163820; without 77824 itself that is 85996, so 77824 is abundant (85996 is more than 77824). Euler's totient φ(77824) = 36864 numbers up to 77824 share no factor with it.
- 4
The digits of 77824 add up to 28, and repeating that until one digit is left gives the digital root 1. The Collatz sequence (halve if even, else 3n+1) takes 32 steps to reach 1.
LaTeX source of the formulas on this page
\[ 77824 = 2^{12} \times 19 \]77824 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 26 |
| Sum of divisors | 163820 |
| Euler totient φ(n) | 36864 |
| Square | 6056574976 |
| Cube | 471346890932224 |
| Square root | 278.969532 (= 64√19) |
| Digit sum / digital root | 28 / 1 |
| Collatz steps to 1 | 32 |
| Scientific notation | 7.7824 × |
77824 in other forms
| Form | Value |
|---|---|
| In words | seventy-seven thousand eight hundred and twenty-four |
| Binary (base 2) | 10011000000000000 |
| Octal (base 8) | 230000 |
| Hexadecimal (base 16) | 13000 |
| Base 3 | 10221202101 |
| As time | 77824 seconds = 21 h 37 min 4 s |
Is 77824 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (77824 ÷ 2 = 38912) | 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 (77824 ÷ 4 = 19456) | 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 | No (remainder 4) | 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 (77824 ÷ 8 = 9728) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 1) | 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 | 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 77824 a prime number?
No. 77824 = × 19, so it is divisible by 2.
What are the factors of 77824?
1, 2, 4, 8, 16, 19, 32, 38, 64, 76, 128, 152, 256, 304, 512, 608, 1024, 1216, 2048, 2432, 4096, 4864, 9728, 19456, 38912, 77824.
What is 77824 in binary?
10011000000000000 (hexadecimal 13000, octal 230000).
What is the square root of 77824?
About 278.9695, exactly 64√19.
Is 77824 divisible by 3?
No. Its digits add up to 28, which is not a multiple of 3.
What is special about the number 77824?
It is a composite number with 26 divisors.