The number 77312
77312 is a composite number with 20 divisors. Its prime factorisation is × 151. Divisors (20): 1, 2, 4, 8, 16, 32, 64, 128, 151, 256, 302, 512, 604, 1208, 2416, 4832 … 77312.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
77312 has no famous special property in the usual lists (prime, square, cube, triangular, Fibonacci, palindrome, perfect), but it is still a composite number.
- 2
77312 is composite. Its prime factorisation is
- 3
The divisors add up to 155496; without 77312 itself that is 78184, so 77312 is abundant (78184 is more than 77312). Euler's totient φ(77312) = 38400 numbers up to 77312 share no factor with it.
- 4
The digits of 77312 add up to 20, and repeating that until one digit is left gives the digital root 2. The Collatz sequence (halve if even, else 3n+1) takes 24 steps to reach 1.
LaTeX source of the formulas on this page
\[ 77312 = 2^{9} \times 151 \]77312 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 20 |
| Sum of divisors | 155496 |
| Euler totient φ(n) | 38400 |
| Square | 5977145344 |
| Cube | 462105060835328 |
| Square root | 278.050355 (= 16√302) |
| Digit sum / digital root | 20 / 2 |
| Collatz steps to 1 | 24 |
| Scientific notation | 7.7312 × |
77312 in other forms
| Form | Value |
|---|---|
| In words | seventy-seven thousand three hundred and twelve |
| Binary (base 2) | 10010111000000000 |
| Octal (base 8) | 227000 |
| Hexadecimal (base 16) | 12E00 |
| Base 3 | 10221001102 |
| As time | 77312 seconds = 21 h 28 min 32 s |
Is 77312 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (77312 ÷ 2 = 38656) | 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 (77312 ÷ 4 = 19328) | 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 4) | 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 (77312 ÷ 8 = 9664) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 2) | 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 | No (remainder 4) | 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 77312 a prime number?
No. 77312 = × 151, so it is divisible by 2.
What are the factors of 77312?
1, 2, 4, 8, 16, 32, 64, 128, 151, 256, 302, 512, 604, 1208, 2416, 4832, 9664, 19328, 38656, 77312.
What is 77312 in binary?
10010111000000000 (hexadecimal 12E00, octal 227000).
What is the square root of 77312?
About 278.0504, exactly 16√302.
Is 77312 divisible by 3?
No. Its digits add up to 20, which is not a multiple of 3.
What is special about the number 77312?
It is a composite number with 20 divisors.