The number 677
677 is the 123rd prime number. Its only divisors are 1 and 677.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 677: the 123rd prime number.
- 2
677 is prime, so its only factors are 1 and 677. It is the 123rd prime; the next prime is 683 and the one before is 673.
- 3
The divisors add up to 678; without 677 itself that is 1, so 677 is deficient (1 is less than 677). Euler's totient φ(677) = 676 numbers up to 677 share no factor with it.
- 4
The digits of 677 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 51 steps to reach 1.
677 at a glance
| Property | Value |
|---|---|
| Type | prime |
| Number of divisors | 2 |
| Sum of divisors | 678 |
| Euler totient φ(n) | 676 |
| Square | 458329 |
| Cube | 310288733 |
| Square root | 26.019224 |
| Digit sum / digital root | 20 / 2 |
| Collatz steps to 1 | 51 |
| Scientific notation | 6.77 × |
677 in other forms
| Form | Value |
|---|---|
| In words | six hundred and seventy-seven |
| Roman numerals | DCLXXVII |
| Binary (base 2) | 1010100101 |
| Octal (base 8) | 1245 |
| Hexadecimal (base 16) | 2A5 |
| Base 3 | 221002 |
| As time | 677 seconds = 11 min 17 s |
Is 677 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 2) | 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 5) | 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 | No (remainder 5) | 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 | No (remainder 7) | 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 5) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 677 a prime number?
Yes. 677 is divisible only by 1 and itself.
What are the factors of 677?
1, 677.
What is 677 in binary?
1010100101 (hexadecimal 2A5, octal 1245).
What is the square root of 677?
About 26.0192.
What is 677 in Roman numerals?
DCLXXVII.
Is 677 divisible by 3?
No. Its digits add up to 20, which is not a multiple of 3.
What is special about the number 677?
677 is the 123rd prime number.