Answer :
173 would be dividable by at least one prime number less than or equal to 173 13.2 if it weren't a prime number. Since 173 cannot be divided evenly by 2, 3, 5, 7, 11, or 13, we know it is a prime number.
173 is a prime number.
Prime factorization: 173 is prime.
The exponent of prime number 173 is 1. Adding 1 to that exponent we get (1 + 1) = 2. Therefore 173 has exactly 2 factors.
Factors of 173: 1, 173
Factor pairs: 173 = 1 x 173
173 has no square factors that allow its square root to be simplified. √173 ≈ 13.1529
If 173 were not a prime number, then it would be divisible by at least one prime number less than or equal to √173 ≈ 13.2. We know that 173 is a prime number since it cannot be divided by 2, 3, 5, 7, 11, or 13 in an equal amount.
To learn more about prime number visit here : https://brainly.com/question/4184435
#SPJ4
173 is prime because it is not divisible by any prime numbers up to its square root, which is approximately 13.15. Only prime numbers less than or equal to 13 needed to be checked, as factors larger than the square root would have been paired with factors smaller than the square root, which have already been ruled out.
To determine whether 173 is a prime number, we need to consider the possibility of it having any prime factors smaller than its square root. The square root of 173 is approximately 13.15. Therefore, any potential factor of 173 must be a prime number less than or equal to 13.
The prime numbers less than or equal to 13 are 2, 3, 5, 7, 11, and 13. Since 173 is not divisible by any of these, we can conclude that 173 has no prime factors other than itself and 1, and is thus a prime number.
Furthermore, considering the fundamental theorem of arithmetic, every integer greater than 1 either is a prime number itself or can be factored into prime numbers.
Since we've established that 173 cannot be divided by any prime number less than or equal to its square root without a remainder, it does not have any prime factorization other than 1 and itself, confirming that it is prime.
