The number 77792
77792 is a composite number with 48 divisors. Its prime factorisation is × 11 × 13 × 17. Divisors (48): 1, 2, 4, 8, 11, 13, 16, 17, 22, 26, 32, 34, 44, 52, 68, 88 … 77792.
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How to work it out
- 1
What is special about 77792: a Harshad number: divisible by its digit sum 32.
- 2
77792 is composite. Its prime factorisation is
- 3
The divisors add up to 190512; without 77792 itself that is 112720, so 77792 is abundant (112720 is more than 77792). Euler's totient φ(77792) = 30720 numbers up to 77792 share no factor with it.
- 4
The digits of 77792 add up to 32, and repeating that until one digit is left gives the digital root 5. The Collatz sequence (halve if even, else 3n+1) takes 169 steps to reach 1.
LaTeX source of the formulas on this page
\[ 77792 = 2^{5} \times 11 \times 13 \times 17 \]77792 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 48 |
| Sum of divisors | 190512 |
| Euler totient φ(n) | 30720 |
| Square | 6051595264 |
| Cube | 470765698777088 |
| Square root | 278.912173 (= 4√4862) |
| Digit sum / digital root | 32 / 5 |
| Collatz steps to 1 | 169 |
| Scientific notation | 7.7792 × |
77792 in other forms
| Form | Value |
|---|---|
| In words | seventy-seven thousand seven hundred and ninety-two |
| Binary (base 2) | 10010111111100000 |
| Octal (base 8) | 227740 |
| Hexadecimal (base 16) | 12FE0 |
| Base 3 | 10221201012 |
| As time | 77792 seconds = 21 h 36 min 32 s |
Is 77792 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (77792 ÷ 2 = 38896) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | No (remainder 2) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (77792 ÷ 4 = 19448) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | No (remainder 2) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | No (remainder 2) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 1) | 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 (77792 ÷ 8 = 9724) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 5) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | No (remainder 2) | A number is divisible by 10 if the last digit is 0. |
| 11 | Yes (77792 ÷ 11 = 7072) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | No (remainder 8) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 77792 a prime number?
No. 77792 = × 11 × 13 × 17, so it is divisible by 2.
What are the factors of 77792?
1, 2, 4, 8, 11, 13, 16, 17, 22, 26, 32, 34, 44, 52, 68, 88, 104, 136, 143, 176, 187, 208, 221, 272, 286, 352, 374, 416, 442, 544, 572, 748, 884, 1144, 1496, 1768, 2288, 2431, 2992, 3536, 4576, 4862, 5984, 7072, 9724, 19448, 38896, 77792.
What is 77792 in binary?
10010111111100000 (hexadecimal 12FE0, octal 227740).
What is the square root of 77792?
About 278.9122, exactly 4√4862.
Is 77792 divisible by 3?
No. Its digits add up to 32, which is not a multiple of 3.
What is special about the number 77792?
77792 is a Harshad number: divisible by its digit sum 32.