The number 77808
77808 is a composite number with 20 divisors. Its prime factorisation is × 3 × 1621. Divisors (20): 1, 2, 3, 4, 6, 8, 12, 16, 24, 48, 1621, 3242, 4863, 6484, 9726, 12968 … 77808.
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How to work it out
- 1
What is special about 77808: a happy number: repeatedly adding the squares of its digits reaches 1.
- 2
77808 is composite. Its prime factorisation is
- 3
The divisors add up to 201128; without 77808 itself that is 123320, so 77808 is abundant (123320 is more than 77808). Euler's totient φ(77808) = 25920 numbers up to 77808 share no factor with it.
- 4
The digits of 77808 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 94 steps to reach 1.
LaTeX source of the formulas on this page
\[ 77808 = 2^{4} \times 3 \times 1621 \]77808 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 20 |
| Sum of divisors | 201128 |
| Euler totient φ(n) | 25920 |
| Square | 6054084864 |
| Cube | 471056235098112 |
| Square root | 278.940854 (= 4√4863) |
| Digit sum / digital root | 30 / 3 |
| Collatz steps to 1 | 94 |
| Scientific notation | 7.7808 × |
77808 in other forms
| Form | Value |
|---|---|
| In words | seventy-seven thousand eight hundred and eight |
| Binary (base 2) | 10010111111110000 |
| Octal (base 8) | 227760 |
| Hexadecimal (base 16) | 12FF0 |
| Base 3 | 10221201210 |
| As time | 77808 seconds = 21 h 36 min 48 s |
Is 77808 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (77808 ÷ 2 = 38904) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (77808 ÷ 3 = 25936) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (77808 ÷ 4 = 19452) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | No (remainder 3) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (77808 ÷ 6 = 12968) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 3) | 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 (77808 ÷ 8 = 9726) | 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 8) | 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 | Yes (77808 ÷ 12 = 6484) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 77808 a prime number?
No. 77808 = × 3 × 1621, so it is divisible by 2.
What are the factors of 77808?
1, 2, 3, 4, 6, 8, 12, 16, 24, 48, 1621, 3242, 4863, 6484, 9726, 12968, 19452, 25936, 38904, 77808.
What is 77808 in binary?
10010111111110000 (hexadecimal 12FF0, octal 227760).
What is the square root of 77808?
About 278.9409, exactly 4√4863.
Is 77808 divisible by 3?
Yes. Its digits add up to 30, a multiple of 3.
What is special about the number 77808?
77808 is a happy number: repeatedly adding the squares of its digits reaches 1.