please can you show me how the get the prime factorization of 392.

thank you

The basic rule is, you need to know the divisibility tests for the first few primes, such as 2,3,5,(7,11,13).

For 392, start by dividing by 2 until the number is odd.
392
=2*196
=2*2*98
=2*2*2*49
Since you know 49=7*7, you would have no problem completing the prime factorization.