The number 77984
77984 is a composite number with 12 divisors. Its prime factorisation is × 2437. Divisors (12): 1, 2, 4, 8, 16, 32, 2437, 4874, 9748, 19496, 38992, 77984.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
77984 has no famous special property in the usual lists (prime, square, cube, triangular, Fibonacci, palindrome, perfect), but it is still a composite number.
- 2
77984 is composite. Its prime factorisation is
- 3
The divisors add up to 153594; without 77984 itself that is 75610, so 77984 is deficient (75610 is less than 77984). Euler's totient φ(77984) = 38976 numbers up to 77984 share no factor with it.
- 4
The digits of 77984 add up to 35, and repeating that until one digit is left gives the digital root 8. The Collatz sequence (halve if even, else 3n+1) takes 138 steps to reach 1.
LaTeX source of the formulas on this page
\[ 77984 = 2^{5} \times 2437 \]77984 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 12 |
| Sum of divisors | 153594 |
| Euler totient φ(n) | 38976 |
| Square | 6081504256 |
| Cube | 474260027899904 |
| Square root | 279.256155 (= 4√4874) |
| Digit sum / digital root | 35 / 8 |
| Collatz steps to 1 | 138 |
| Scientific notation | 7.7984 × |
77984 in other forms
| Form | Value |
|---|---|
| In words | seventy-seven thousand nine hundred and eighty-four |
| Binary (base 2) | 10011000010100000 |
| Octal (base 8) | 230240 |
| Hexadecimal (base 16) | 130A0 |
| Base 3 | 10221222022 |
| As time | 77984 seconds = 21 h 39 min 44 s |
Is 77984 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (77984 ÷ 2 = 38992) | 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 (77984 ÷ 4 = 19496) | 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 | 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 (77984 ÷ 8 = 9748) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 8) | 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 5) | 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 77984 a prime number?
No. 77984 = × 2437, so it is divisible by 2.
What are the factors of 77984?
1, 2, 4, 8, 16, 32, 2437, 4874, 9748, 19496, 38992, 77984.
What is 77984 in binary?
10011000010100000 (hexadecimal 130A0, octal 230240).
What is the square root of 77984?
About 279.2562, exactly 4√4874.
Is 77984 divisible by 3?
No. Its digits add up to 35, which is not a multiple of 3.
What is special about the number 77984?
It is a composite number with 12 divisors.