The number 77128
77128 is a composite number with 16 divisors. Its prime factorisation is × 31 × 311. Divisors (16): 1, 2, 4, 8, 31, 62, 124, 248, 311, 622, 1244, 2488, 9641, 19282, 38564, 77128.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 77128: a happy number: repeatedly adding the squares of its digits reaches 1.
- 2
77128 is composite. Its prime factorisation is
- 3
The divisors add up to 149760; without 77128 itself that is 72632, so 77128 is deficient (72632 is less than 77128). Euler's totient φ(77128) = 37200 numbers up to 77128 share no factor with it.
- 4
The digits of 77128 add up to 25, and repeating that until one digit is left gives the digital root 7. The Collatz sequence (halve if even, else 3n+1) takes 76 steps to reach 1.
LaTeX source of the formulas on this page
\[ 77128 = 2^{3} \times 31 \times 311 \]77128 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 16 |
| Sum of divisors | 149760 |
| Euler totient φ(n) | 37200 |
| Square | 5948728384 |
| Cube | 458813522801152 |
| Square root | 277.719283 (= 2√19282) |
| Digit sum / digital root | 25 / 7 |
| Collatz steps to 1 | 76 |
| Scientific notation | 7.7128 × |
77128 in other forms
| Form | Value |
|---|---|
| In words | seventy-seven thousand one hundred and twenty-eight |
| Binary (base 2) | 10010110101001000 |
| Octal (base 8) | 226510 |
| Hexadecimal (base 16) | 12D48 |
| Base 3 | 10220210121 |
| As time | 77128 seconds = 21 h 25 min 28 s |
Is 77128 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (77128 ÷ 2 = 38564) | 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 (77128 ÷ 4 = 19282) | 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 (77128 ÷ 8 = 9641) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 7) | 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 | No (remainder 7) | 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 77128 a prime number?
No. 77128 = × 31 × 311, so it is divisible by 2.
What are the factors of 77128?
1, 2, 4, 8, 31, 62, 124, 248, 311, 622, 1244, 2488, 9641, 19282, 38564, 77128.
What is 77128 in binary?
10010110101001000 (hexadecimal 12D48, octal 226510).
What is the square root of 77128?
About 277.7193, exactly 2√19282.
Is 77128 divisible by 3?
No. Its digits add up to 25, which is not a multiple of 3.
What is special about the number 77128?
77128 is a happy number: repeatedly adding the squares of its digits reaches 1.