The number 77200
77200 is a composite number with 30 divisors. Its prime factorisation is × × 193. Divisors (30): 1, 2, 4, 5, 8, 10, 16, 20, 25, 40, 50, 80, 100, 193, 200, 386 … 77200.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 77200: a Harshad number: divisible by its digit sum 16.
- 2
77200 is composite. Its prime factorisation is
- 3
The divisors add up to 186434; without 77200 itself that is 109234, so 77200 is abundant (109234 is more than 77200). Euler's totient φ(77200) = 30720 numbers up to 77200 share no factor with it.
- 4
The digits of 77200 add up to 16, and repeating that until one digit is left gives the digital root 7. The Collatz sequence (halve if even, else 3n+1) takes 63 steps to reach 1.
LaTeX source of the formulas on this page
\[ 77200 = 2^{4} \times 5^{2} \times 193 \]77200 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 30 |
| Sum of divisors | 186434 |
| Euler totient φ(n) | 30720 |
| Square | 5959840000 |
| Cube | 460099648000000 |
| Square root | 277.848880 (= 20√193) |
| Digit sum / digital root | 16 / 7 |
| Collatz steps to 1 | 63 |
| Scientific notation | 7.72 × |
77200 in other forms
| Form | Value |
|---|---|
| In words | seventy-seven thousand two hundred |
| Binary (base 2) | 10010110110010000 |
| Octal (base 8) | 226620 |
| Hexadecimal (base 16) | 12D90 |
| Base 3 | 10220220021 |
| As time | 77200 seconds = 21 h 26 min 40 s |
Is 77200 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (77200 ÷ 2 = 38600) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | No (remainder 1) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (77200 ÷ 4 = 19300) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | Yes (77200 ÷ 5 = 15440) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | No (remainder 4) | 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 (77200 ÷ 8 = 9650) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 7) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | Yes (77200 ÷ 10 = 7720) | 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 | No (remainder 4) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 77200 a prime number?
No. 77200 = × × 193, so it is divisible by 2.
What are the factors of 77200?
1, 2, 4, 5, 8, 10, 16, 20, 25, 40, 50, 80, 100, 193, 200, 386, 400, 772, 965, 1544, 1930, 3088, 3860, 4825, 7720, 9650, 15440, 19300, 38600, 77200.
What is 77200 in binary?
10010110110010000 (hexadecimal 12D90, octal 226620).
What is the square root of 77200?
About 277.8489, exactly 20√193.
Is 77200 divisible by 3?
No. Its digits add up to 16, which is not a multiple of 3.
What is special about the number 77200?
77200 is a Harshad number: divisible by its digit sum 16.