The number 577
577 is the 106th prime number. Its only divisors are 1 and 577.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 577: the 106th prime number.
- 2
577 is prime, so its only factors are 1 and 577. It is the 106th prime; the next prime is 587 and the one before is 571.
- 3
The divisors add up to 578; without 577 itself that is 1, so 577 is deficient (1 is less than 577). Euler's totient φ(577) = 576 numbers up to 577 share no factor with it.
- 4
The digits of 577 add up to 19, and repeating that until one digit is left gives the digital root 1. The Collatz sequence (halve if even, else 3n+1) takes 30 steps to reach 1.
577 at a glance
| Property | Value |
|---|---|
| Type | prime |
| Number of divisors | 2 |
| Sum of divisors | 578 |
| Euler totient φ(n) | 576 |
| Square | 332929 |
| Cube | 192100033 |
| Square root | 24.020824 |
| Digit sum / digital root | 19 / 1 |
| Collatz steps to 1 | 30 |
| Scientific notation | 5.77 × |
577 in other forms
| Form | Value |
|---|---|
| In words | five hundred and seventy-seven |
| Roman numerals | DLXXVII |
| Binary (base 2) | 1001000001 |
| Octal (base 8) | 1101 |
| Hexadecimal (base 16) | 241 |
| Base 3 | 210101 |
| As time | 577 seconds = 9 min 37 s |
Is 577 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | No (remainder 1) | 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 | No (remainder 1) | 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 | No (remainder 1) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 3) | 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 | No (remainder 1) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 1) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | No (remainder 7) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 5) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | No (remainder 1) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 577 a prime number?
Yes. 577 is divisible only by 1 and itself.
What are the factors of 577?
1, 577.
What is 577 in binary?
1001000001 (hexadecimal 241, octal 1101).
What is the square root of 577?
About 24.0208.
What is 577 in Roman numerals?
DLXXVII.
Is 577 divisible by 3?
No. Its digits add up to 19, which is not a multiple of 3.
What is special about the number 577?
577 is the 106th prime number.