The number 77820
77820 is a composite number with 24 divisors. Its prime factorisation is × 3 × 5 × 1297. Divisors (24): 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60, 1297, 2594, 3891, 5188 … 77820.
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How to work it out
- 1
77820 has no famous special property in the usual lists (prime, square, cube, triangular, Fibonacci, palindrome, perfect), but it is still a composite number.
- 2
77820 is composite. Its prime factorisation is
- 3
The divisors add up to 218064; without 77820 itself that is 140244, so 77820 is abundant (140244 is more than 77820). Euler's totient φ(77820) = 20736 numbers up to 77820 share no factor with it.
- 4
The digits of 77820 add up to 24, and repeating that until one digit is left gives the digital root 6. The Collatz sequence (halve if even, else 3n+1) takes 94 steps to reach 1.
LaTeX source of the formulas on this page
\[ 77820 = 2^{2} \times 3 \times 5 \times 1297 \]77820 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 24 |
| Sum of divisors | 218064 |
| Euler totient φ(n) | 20736 |
| Square | 6055952400 |
| Cube | 471274215768000 |
| Square root | 278.962363 (= 2√19455) |
| Digit sum / digital root | 24 / 6 |
| Collatz steps to 1 | 94 |
| Scientific notation | 7.782 × |
77820 in other forms
| Form | Value |
|---|---|
| In words | seventy-seven thousand eight hundred and twenty |
| Binary (base 2) | 10010111111111100 |
| Octal (base 8) | 227774 |
| Hexadecimal (base 16) | 12FFC |
| Base 3 | 10221202020 |
| As time | 77820 seconds = 21 h 37 min 0 s |
Is 77820 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (77820 ÷ 2 = 38910) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (77820 ÷ 3 = 25940) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (77820 ÷ 4 = 19455) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | Yes (77820 ÷ 5 = 15564) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (77820 ÷ 6 = 12970) | 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 | No (remainder 4) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 6) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | Yes (77820 ÷ 10 = 7782) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 6) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (77820 ÷ 12 = 6485) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 77820 a prime number?
No. 77820 = × 3 × 5 × 1297, so it is divisible by 2.
What are the factors of 77820?
1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60, 1297, 2594, 3891, 5188, 6485, 7782, 12970, 15564, 19455, 25940, 38910, 77820.
What is 77820 in binary?
10010111111111100 (hexadecimal 12FFC, octal 227774).
What is the square root of 77820?
About 278.9624, exactly 2√19455.
Is 77820 divisible by 3?
Yes. Its digits add up to 24, a multiple of 3.
What is special about the number 77820?
It is a composite number with 24 divisors.