The number 77680
77680 is a composite number with 20 divisors. Its prime factorisation is × 5 × 971. Divisors (20): 1, 2, 4, 5, 8, 10, 16, 20, 40, 80, 971, 1942, 3884, 4855, 7768, 9710 … 77680.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
77680 has no famous special property in the usual lists (prime, square, cube, triangular, Fibonacci, palindrome, perfect), but it is still a composite number.
- 2
77680 is composite. Its prime factorisation is
- 3
The divisors add up to 180792; without 77680 itself that is 103112, so 77680 is abundant (103112 is more than 77680). Euler's totient φ(77680) = 31040 numbers up to 77680 share no factor with it.
- 4
The digits of 77680 add up to 28, and repeating that until one digit is left gives the digital root 1. The Collatz sequence (halve if even, else 3n+1) takes 125 steps to reach 1.
LaTeX source of the formulas on this page
\[ 77680 = 2^{4} \times 5 \times 971 \]77680 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 20 |
| Sum of divisors | 180792 |
| Euler totient φ(n) | 31040 |
| Square | 6034182400 |
| Cube | 468735288832000 |
| Square root | 278.711320 (= 4√4855) |
| Digit sum / digital root | 28 / 1 |
| Collatz steps to 1 | 125 |
| Scientific notation | 7.768 × |
77680 in other forms
| Form | Value |
|---|---|
| In words | seventy-seven thousand six hundred and eighty |
| Binary (base 2) | 10010111101110000 |
| Octal (base 8) | 227560 |
| Hexadecimal (base 16) | 12F70 |
| Base 3 | 10221120001 |
| As time | 77680 seconds = 21 h 34 min 40 s |
Is 77680 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (77680 ÷ 2 = 38840) | 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 (77680 ÷ 4 = 19420) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | Yes (77680 ÷ 5 = 15536) | 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 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 (77680 ÷ 8 = 9710) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 1) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | Yes (77680 ÷ 10 = 7768) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 9) | 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 77680 a prime number?
No. 77680 = × 5 × 971, so it is divisible by 2.
What are the factors of 77680?
1, 2, 4, 5, 8, 10, 16, 20, 40, 80, 971, 1942, 3884, 4855, 7768, 9710, 15536, 19420, 38840, 77680.
What is 77680 in binary?
10010111101110000 (hexadecimal 12F70, octal 227560).
What is the square root of 77680?
About 278.7113, exactly 4√4855.
Is 77680 divisible by 3?
No. Its digits add up to 28, which is not a multiple of 3.
What is special about the number 77680?
It is a composite number with 20 divisors.