The number 77120
77120 is a composite number with 28 divisors. Its prime factorisation is × 5 × 241. Divisors (28): 1, 2, 4, 5, 8, 10, 16, 20, 32, 40, 64, 80, 160, 241, 320, 482 … 77120.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 77120: a happy number: repeatedly adding the squares of its digits reaches 1.
- 2
77120 is composite. Its prime factorisation is
- 3
The divisors add up to 184404; without 77120 itself that is 107284, so 77120 is abundant (107284 is more than 77120). Euler's totient φ(77120) = 30720 numbers up to 77120 share no factor with it.
- 4
The digits of 77120 add up to 17, and repeating that until one digit is left gives the digital root 8. The Collatz sequence (halve if even, else 3n+1) takes 24 steps to reach 1.
LaTeX source of the formulas on this page
\[ 77120 = 2^{6} \times 5 \times 241 \]77120 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 28 |
| Sum of divisors | 184404 |
| Euler totient φ(n) | 30720 |
| Square | 5947494400 |
| Cube | 458670768128000 |
| Square root | 277.704879 (= 8√1205) |
| Digit sum / digital root | 17 / 8 |
| Collatz steps to 1 | 24 |
| Scientific notation | 7.712 × |
77120 in other forms
| Form | Value |
|---|---|
| In words | seventy-seven thousand one hundred and twenty |
| Binary (base 2) | 10010110101000000 |
| Octal (base 8) | 226500 |
| Hexadecimal (base 16) | 12D40 |
| Base 3 | 10220210022 |
| As time | 77120 seconds = 21 h 25 min 20 s |
Is 77120 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (77120 ÷ 2 = 38560) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | No (remainder 2) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (77120 ÷ 4 = 19280) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | Yes (77120 ÷ 5 = 15424) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | No (remainder 2) | 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 (77120 ÷ 8 = 9640) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 8) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | Yes (77120 ÷ 10 = 7712) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 10) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | No (remainder 8) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 77120 a prime number?
No. 77120 = × 5 × 241, so it is divisible by 2.
What are the factors of 77120?
1, 2, 4, 5, 8, 10, 16, 20, 32, 40, 64, 80, 160, 241, 320, 482, 964, 1205, 1928, 2410, 3856, 4820, 7712, 9640, 15424, 19280, 38560, 77120.
What is 77120 in binary?
10010110101000000 (hexadecimal 12D40, octal 226500).
What is the square root of 77120?
About 277.7049, exactly 8√1205.
Is 77120 divisible by 3?
No. Its digits add up to 17, which is not a multiple of 3.
What is special about the number 77120?
77120 is a happy number: repeatedly adding the squares of its digits reaches 1.