The number 77112
77112 is a composite number with 80 divisors. Its prime factorisation is × × 7 × 17. Divisors (80): 1, 2, 3, 4, 6, 7, 8, 9, 12, 14, 17, 18, 21, 24, 27, 28 … 77112.
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How to work it out
- 1
What is special about 77112: a Harshad number: divisible by its digit sum 18.
- 2
77112 is composite. Its prime factorisation is
- 3
The divisors add up to 261360; without 77112 itself that is 184248, so 77112 is abundant (184248 is more than 77112). Euler's totient φ(77112) = 20736 numbers up to 77112 share no factor with it.
- 4
The digits of 77112 add up to 18, and repeating that until one digit is left gives the digital root 9. The Collatz sequence (halve if even, else 3n+1) takes 138 steps to reach 1.
LaTeX source of the formulas on this page
\[ 77112 = 2^{3} \times 3^{4} \times 7 \times 17 \]77112 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 80 |
| Sum of divisors | 261360 |
| Euler totient φ(n) | 20736 |
| Square | 5946260544 |
| Cube | 458528043068928 |
| Square root | 277.690475 (= 18√238) |
| Digit sum / digital root | 18 / 9 |
| Collatz steps to 1 | 138 |
| Scientific notation | 7.7112 × |
77112 in other forms
| Form | Value |
|---|---|
| In words | seventy-seven thousand one hundred and twelve |
| Binary (base 2) | 10010110100111000 |
| Octal (base 8) | 226470 |
| Hexadecimal (base 16) | 12D38 |
| Base 3 | 10220210000 |
| As time | 77112 seconds = 21 h 25 min 12 s |
Is 77112 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (77112 ÷ 2 = 38556) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (77112 ÷ 3 = 25704) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (77112 ÷ 4 = 19278) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | No (remainder 2) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (77112 ÷ 6 = 12852) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | Yes (77112 ÷ 7 = 11016) | 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 (77112 ÷ 8 = 9639) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | Yes (77112 ÷ 9 = 8568) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | No (remainder 2) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 2) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (77112 ÷ 12 = 6426) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 77112 a prime number?
No. 77112 = × × 7 × 17, so it is divisible by 2.
What are the factors of 77112?
1, 2, 3, 4, 6, 7, 8, 9, 12, 14, 17, 18, 21, 24, 27, 28, 34, 36, 42, 51, 54, 56, 63, 68, 72, 81, 84, 102, 108, 119, 126, 136, 153, 162, 168, 189, 204, 216, 238, 252, 306, 324, 357, 378, 408, 459, 476, 504, 567, 612, 648, 714, 756, 918, 952, 1071, 1134, 1224, 1377, 1428, 1512, 1836, 2142, 2268, 2754, 2856, 3213, 3672, 4284, 4536, 5508, 6426, 8568, 9639, 11016, 12852, 19278, 25704, 38556, 77112.
What is 77112 in binary?
10010110100111000 (hexadecimal 12D38, octal 226470).
What is the square root of 77112?
About 277.6905, exactly 18√238.
Is 77112 divisible by 3?
Yes. Its digits add up to 18, a multiple of 3.
What is special about the number 77112?
77112 is a Harshad number: divisible by its digit sum 18.