The number 77088
77088 is a composite number with 48 divisors. Its prime factorisation is × 3 × 11 × 73. Divisors (48): 1, 2, 3, 4, 6, 8, 11, 12, 16, 22, 24, 32, 33, 44, 48, 66 … 77088.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 77088: a happy number: repeatedly adding the squares of its digits reaches 1.
- 2
77088 is composite. Its prime factorisation is
- 3
The divisors add up to 223776; without 77088 itself that is 146688, so 77088 is abundant (146688 is more than 77088). Euler's totient φ(77088) = 23040 numbers up to 77088 share no factor with it.
- 4
The digits of 77088 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
\[ 77088 = 2^{5} \times 3 \times 11 \times 73 \]77088 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 48 |
| Sum of divisors | 223776 |
| Euler totient φ(n) | 23040 |
| Square | 5942559744 |
| Cube | 458100045545472 |
| Square root | 277.647258 (= 4√4818) |
| Digit sum / digital root | 30 / 3 |
| Collatz steps to 1 | 125 |
| Scientific notation | 7.7088 × |
77088 in other forms
| Form | Value |
|---|---|
| In words | seventy-seven thousand and eighty-eight |
| Binary (base 2) | 10010110100100000 |
| Octal (base 8) | 226440 |
| Hexadecimal (base 16) | 12D20 |
| Base 3 | 10220202010 |
| As time | 77088 seconds = 21 h 24 min 48 s |
Is 77088 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (77088 ÷ 2 = 38544) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (77088 ÷ 3 = 25696) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (77088 ÷ 4 = 19272) | 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 (77088 ÷ 6 = 12848) | 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 (77088 ÷ 8 = 9636) | 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 | Yes (77088 ÷ 11 = 7008) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (77088 ÷ 12 = 6424) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 77088 a prime number?
No. 77088 = × 3 × 11 × 73, so it is divisible by 2.
What are the factors of 77088?
1, 2, 3, 4, 6, 8, 11, 12, 16, 22, 24, 32, 33, 44, 48, 66, 73, 88, 96, 132, 146, 176, 219, 264, 292, 352, 438, 528, 584, 803, 876, 1056, 1168, 1606, 1752, 2336, 2409, 3212, 3504, 4818, 6424, 7008, 9636, 12848, 19272, 25696, 38544, 77088.
What is 77088 in binary?
10010110100100000 (hexadecimal 12D20, octal 226440).
What is the square root of 77088?
About 277.6473, exactly 4√4818.
Is 77088 divisible by 3?
Yes. Its digits add up to 30, a multiple of 3.
What is special about the number 77088?
77088 is a happy number: repeatedly adding the squares of its digits reaches 1.