The number 673
673 is the 122nd prime number. Its only divisors are 1 and 673.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 673: the 122nd prime number; a happy number: repeatedly adding the squares of its digits reaches 1.
- 2
673 is prime, so its only factors are 1 and 673. It is the 122nd prime; the next prime is 677 and the one before is 661.
- 3
The divisors add up to 674; without 673 itself that is 1, so 673 is deficient (1 is less than 673). Euler's totient φ(673) = 672 numbers up to 673 share no factor with it.
- 4
The digits of 673 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 64 steps to reach 1.
673 at a glance
| Property | Value |
|---|---|
| Type | prime |
| Number of divisors | 2 |
| Sum of divisors | 674 |
| Euler totient φ(n) | 672 |
| Square | 452929 |
| Cube | 304821217 |
| Square root | 25.942244 |
| Digit sum / digital root | 16 / 7 |
| Collatz steps to 1 | 64 |
| Scientific notation | 6.73 × |
673 in other forms
| Form | Value |
|---|---|
| In words | six hundred and seventy-three |
| Roman numerals | DCLXXIII |
| Binary (base 2) | 1010100001 |
| Octal (base 8) | 1241 |
| Hexadecimal (base 16) | 2A1 |
| Base 3 | 220221 |
| As time | 673 seconds = 11 min 13 s |
Is 673 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 3) | 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 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 | No (remainder 1) | 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 | No (remainder 3) | 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 1) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 673 a prime number?
Yes. 673 is divisible only by 1 and itself.
What are the factors of 673?
1, 673.
What is 673 in binary?
1010100001 (hexadecimal 2A1, octal 1241).
What is the square root of 673?
About 25.9422.
What is 673 in Roman numerals?
DCLXXIII.
Is 673 divisible by 3?
No. Its digits add up to 16, which is not a multiple of 3.
What is special about the number 673?
673 is the 122nd prime number; a happy number: repeatedly adding the squares of its digits reaches 1.