The number 77968
77968 is a composite number with 20 divisors. Its prime factorisation is × 11 × 443. Divisors (20): 1, 2, 4, 8, 11, 16, 22, 44, 88, 176, 443, 886, 1772, 3544, 4873, 7088 … 77968.
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How to work it out
- 1
77968 has no famous special property in the usual lists (prime, square, cube, triangular, Fibonacci, palindrome, perfect), but it is still a composite number.
- 2
77968 is composite. Its prime factorisation is
- 3
The divisors add up to 165168; without 77968 itself that is 87200, so 77968 is abundant (87200 is more than 77968). Euler's totient φ(77968) = 35360 numbers up to 77968 share no factor with it.
- 4
The digits of 77968 add up to 37, and repeating that until one digit is left gives the digital root 1. The Collatz sequence (halve if even, else 3n+1) takes 125 steps to reach 1.
LaTeX source of the formulas on this page
\[ 77968 = 2^{4} \times 11 \times 443 \]77968 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 20 |
| Sum of divisors | 165168 |
| Euler totient φ(n) | 35360 |
| Square | 6079009024 |
| Cube | 473968175583232 |
| Square root | 279.227506 (= 4√4873) |
| Digit sum / digital root | 37 / 1 |
| Collatz steps to 1 | 125 |
| Scientific notation | 7.7968 × |
77968 in other forms
| Form | Value |
|---|---|
| In words | seventy-seven thousand nine hundred and sixty-eight |
| Binary (base 2) | 10011000010010000 |
| Octal (base 8) | 230220 |
| Hexadecimal (base 16) | 13090 |
| Base 3 | 10221221201 |
| As time | 77968 seconds = 21 h 39 min 28 s |
Is 77968 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (77968 ÷ 2 = 38984) | 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 (77968 ÷ 4 = 19492) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | No (remainder 3) | 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 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 (77968 ÷ 8 = 9746) | 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 8) | A number is divisible by 10 if the last digit is 0. |
| 11 | Yes (77968 ÷ 11 = 7088) | 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 77968 a prime number?
No. 77968 = × 11 × 443, so it is divisible by 2.
What are the factors of 77968?
1, 2, 4, 8, 11, 16, 22, 44, 88, 176, 443, 886, 1772, 3544, 4873, 7088, 9746, 19492, 38984, 77968.
What is 77968 in binary?
10011000010010000 (hexadecimal 13090, octal 230220).
What is the square root of 77968?
About 279.2275, exactly 4√4873.
Is 77968 divisible by 3?
No. Its digits add up to 37, which is not a multiple of 3.
What is special about the number 77968?
It is a composite number with 20 divisors.