Problem 17 - Introductory Algebra for College Students

Question

Identify each natural number as prime or composite. If the number is composite, find its prime factorization. $$37$$

Step-by-Step Solution

Answer

The number 37 is a prime number. Hence, its prime factorization is not required.

Step 1: Checking if the number is prime

To determine if 37 is a prime number, it can be checked if it has any divisors other than 1 and itself. This can be done by trying to divide it by all numbers up to its square root (since a larger factor of the number would be a multiple of smaller factor that has already been checked).

Step 2: Conclusion

In this case, it is found that 37 has no divisors other than 1 and itself, so it's a prime number. Therefore, there is no need to find the prime factorization.