The number 77664
77664 is a composite number with 24 divisors. Its prime factorisation is × 3 × 809. Divisors (24): 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 96, 809, 1618, 2427, 3236 … 77664.
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How to work it out
- 1
77664 has no famous special property in the usual lists (prime, square, cube, triangular, Fibonacci, palindrome, perfect), but it is still a composite number.
- 2
77664 is composite. Its prime factorisation is
- 3
The divisors add up to 204120; without 77664 itself that is 126456, so 77664 is abundant (126456 is more than 77664). Euler's totient φ(77664) = 25856 numbers up to 77664 share no factor with it.
- 4
The digits of 77664 add up to 30, and repeating that until one digit is left gives the digital root 3. The Collatz sequence (halve if even, else 3n+1) takes 125 steps to reach 1.
LaTeX source of the formulas on this page
\[ 77664 = 2^{5} \times 3 \times 809 \]77664 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 24 |
| Sum of divisors | 204120 |
| Euler totient φ(n) | 25856 |
| Square | 6031696896 |
| Cube | 468445707730944 |
| Square root | 278.682615 (= 4√4854) |
| Digit sum / digital root | 30 / 3 |
| Collatz steps to 1 | 125 |
| Scientific notation | 7.7664 × |
77664 in other forms
| Form | Value |
|---|---|
| In words | seventy-seven thousand six hundred and sixty-four |
| Binary (base 2) | 10010111101100000 |
| Octal (base 8) | 227540 |
| Hexadecimal (base 16) | 12F60 |
| Base 3 | 10221112110 |
| As time | 77664 seconds = 21 h 34 min 24 s |
Is 77664 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (77664 ÷ 2 = 38832) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (77664 ÷ 3 = 25888) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (77664 ÷ 4 = 19416) | 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 (77664 ÷ 6 = 12944) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 6) | 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 (77664 ÷ 8 = 9708) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 3) | 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 4) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (77664 ÷ 12 = 6472) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 77664 a prime number?
No. 77664 = × 3 × 809, so it is divisible by 2.
What are the factors of 77664?
1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 96, 809, 1618, 2427, 3236, 4854, 6472, 9708, 12944, 19416, 25888, 38832, 77664.
What is 77664 in binary?
10010111101100000 (hexadecimal 12F60, octal 227540).
What is the square root of 77664?
About 278.6826, exactly 4√4854.
Is 77664 divisible by 3?
Yes. Its digits add up to 30, a multiple of 3.
What is special about the number 77664?
It is a composite number with 24 divisors.