The number 77600
77600 is a composite number with 36 divisors. Its prime factorisation is × × 97. Divisors (36): 1, 2, 4, 5, 8, 10, 16, 20, 25, 32, 40, 50, 80, 97, 100, 160 … 77600.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 77600: a Harshad number: divisible by its digit sum 20.
- 2
77600 is composite. Its prime factorisation is
- 3
The divisors add up to 191394; without 77600 itself that is 113794, so 77600 is abundant (113794 is more than 77600). Euler's totient φ(77600) = 30720 numbers up to 77600 share no factor with it.
- 4
The digits of 77600 add up to 20, and repeating that until one digit is left gives the digital root 2. The Collatz sequence (halve if even, else 3n+1) takes 169 steps to reach 1.
LaTeX source of the formulas on this page
\[ 77600 = 2^{5} \times 5^{2} \times 97 \]77600 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 36 |
| Sum of divisors | 191394 |
| Euler totient φ(n) | 30720 |
| Square | 6021760000 |
| Cube | 467288576000000 |
| Square root | 278.567766 (= 20√194) |
| Digit sum / digital root | 20 / 2 |
| Collatz steps to 1 | 169 |
| Scientific notation | 7.76 × |
77600 in other forms
| Form | Value |
|---|---|
| In words | seventy-seven thousand six hundred |
| Binary (base 2) | 10010111100100000 |
| Octal (base 8) | 227440 |
| Hexadecimal (base 16) | 12F20 |
| Base 3 | 10221110002 |
| As time | 77600 seconds = 21 h 33 min 20 s |
Is 77600 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (77600 ÷ 2 = 38800) | 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 (77600 ÷ 4 = 19400) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | Yes (77600 ÷ 5 = 15520) | 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 5) | 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 (77600 ÷ 8 = 9700) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 2) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | Yes (77600 ÷ 10 = 7760) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 6) | 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 77600 a prime number?
No. 77600 = × × 97, so it is divisible by 2.
What are the factors of 77600?
1, 2, 4, 5, 8, 10, 16, 20, 25, 32, 40, 50, 80, 97, 100, 160, 194, 200, 388, 400, 485, 776, 800, 970, 1552, 1940, 2425, 3104, 3880, 4850, 7760, 9700, 15520, 19400, 38800, 77600.
What is 77600 in binary?
10010111100100000 (hexadecimal 12F20, octal 227440).
What is the square root of 77600?
About 278.5678, exactly 20√194.
Is 77600 divisible by 3?
No. Its digits add up to 20, which is not a multiple of 3.
What is special about the number 77600?
77600 is a Harshad number: divisible by its digit sum 20.