The number 77904
77904 is a composite number with 30 divisors. Its prime factorisation is × × 541. Divisors (30): 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 36, 48, 72, 144, 541 … 77904.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
77904 has no famous special property in the usual lists (prime, square, cube, triangular, Fibonacci, palindrome, perfect), but it is still a composite number.
- 2
77904 is composite. Its prime factorisation is
- 3
The divisors add up to 218426; without 77904 itself that is 140522, so 77904 is abundant (140522 is more than 77904). Euler's totient φ(77904) = 25920 numbers up to 77904 share no factor with it.
- 4
The digits of 77904 add up to 27, and repeating that until one digit is left gives the digital root 9. The Collatz sequence (halve if even, else 3n+1) takes 138 steps to reach 1.
LaTeX source of the formulas on this page
\[ 77904 = 2^{4} \times 3^{2} \times 541 \]77904 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 30 |
| Sum of divisors | 218426 |
| Euler totient φ(n) | 25920 |
| Square | 6069033216 |
| Cube | 472801963659264 |
| Square root | 279.112880 (= 12√541) |
| Digit sum / digital root | 27 / 9 |
| Collatz steps to 1 | 138 |
| Scientific notation | 7.7904 × |
77904 in other forms
| Form | Value |
|---|---|
| In words | seventy-seven thousand nine hundred and four |
| Binary (base 2) | 10011000001010000 |
| Octal (base 8) | 230120 |
| Hexadecimal (base 16) | 13050 |
| Base 3 | 10221212100 |
| As time | 77904 seconds = 21 h 38 min 24 s |
Is 77904 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (77904 ÷ 2 = 38952) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (77904 ÷ 3 = 25968) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (77904 ÷ 4 = 19476) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | No (remainder 4) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (77904 ÷ 6 = 12984) | 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 (77904 ÷ 8 = 9738) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | Yes (77904 ÷ 9 = 8656) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | No (remainder 4) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 2) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (77904 ÷ 12 = 6492) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 77904 a prime number?
No. 77904 = × × 541, so it is divisible by 2.
What are the factors of 77904?
1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 36, 48, 72, 144, 541, 1082, 1623, 2164, 3246, 4328, 4869, 6492, 8656, 9738, 12984, 19476, 25968, 38952, 77904.
What is 77904 in binary?
10011000001010000 (hexadecimal 13050, octal 230120).
What is the square root of 77904?
About 279.1129, exactly 12√541.
Is 77904 divisible by 3?
Yes. Its digits add up to 27, a multiple of 3.
What is special about the number 77904?
It is a composite number with 30 divisors.