To factor 93 into a product of its prime numbers:

1. Check for divisibility by small prime numbers.
2. 93 is an odd number, so it's not divisible by 2.
3. Sum of digits of 93 is 9 + 3 = 12, which is divisible by 3. So, 93 is divisible by 3.

Dividing 93 by 3 gives: $93 \div 3 = 31$

Now, 31 is a prime number, so it cannot be factored further.

Thus, the prime factorization of 93 is: $93 = 3 \times 31$

Would you like more details, or do you have any questions?

1. What is the general process for prime factorization?
2. How can you check if a number is prime?
3. Why is prime factorization useful in mathematics?
4. Can you factor larger composite numbers similarly?
5. What are some applications of prime factorization in real life?

Tip: For quick divisibility checks, remember that a number is divisible by 3 if the sum of its digits is divisible by 3.