The number 77296
77296 is a composite number with 10 divisors. Its prime factorisation is × 4831. Divisors (10): 1, 2, 4, 8, 16, 4831, 9662, 19324, 38648, 77296.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 77296: a happy number: repeatedly adding the squares of its digits reaches 1.
- 2
77296 is composite. Its prime factorisation is
- 3
The divisors add up to 149792; without 77296 itself that is 72496, so 77296 is deficient (72496 is less than 77296). Euler's totient φ(77296) = 38640 numbers up to 77296 share no factor with it.
- 4
The digits of 77296 add up to 31, and repeating that until one digit is left gives the digital root 4. The Collatz sequence (halve if even, else 3n+1) takes 125 steps to reach 1.
LaTeX source of the formulas on this page
\[ 77296 = 2^{4} \times 4831 \]77296 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 10 |
| Sum of divisors | 149792 |
| Euler totient φ(n) | 38640 |
| Square | 5974671616 |
| Cube | 461818217230336 |
| Square root | 278.021582 (= 4√4831) |
| Digit sum / digital root | 31 / 4 |
| Collatz steps to 1 | 125 |
| Scientific notation | 7.7296 × |
77296 in other forms
| Form | Value |
|---|---|
| In words | seventy-seven thousand two hundred and ninety-six |
| Binary (base 2) | 10010110111110000 |
| Octal (base 8) | 226760 |
| Hexadecimal (base 16) | 12DF0 |
| Base 3 | 10221000211 |
| As time | 77296 seconds = 21 h 28 min 16 s |
Is 77296 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (77296 ÷ 2 = 38648) | 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 (77296 ÷ 4 = 19324) | 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 | 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 (77296 ÷ 8 = 9662) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 4) | 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 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 77296 a prime number?
No. 77296 = × 4831, so it is divisible by 2.
What are the factors of 77296?
1, 2, 4, 8, 16, 4831, 9662, 19324, 38648, 77296.
What is 77296 in binary?
10010110111110000 (hexadecimal 12DF0, octal 226760).
What is the square root of 77296?
About 278.0216, exactly 4√4831.
Is 77296 divisible by 3?
No. Its digits add up to 31, which is not a multiple of 3.
What is special about the number 77296?
77296 is a happy number: repeatedly adding the squares of its digits reaches 1.