In order to factor a number, you have to try and check if it's divisible by all the possible primes, starting with the smaller ones.
So, we begin: 50 is divisible by 2 (the first prime), and we have
[tex]50\div 2=25[/tex]
25 is not divisible by 2 nor by 3 (the next prime), so we try the next prime, which is 5. 25 is divisible by 5, and we have
[tex]25\div 5=5[/tex]
Finally, 5 is itself a prime, and we have
[tex]5\div 5=1[/tex]
So, we started from 50 and we finished at 1. To do so, we divided by 2 once and by 5 twice. This means that there are two "5"s and one "2" inside 50, and thus its prime factorization is
[tex]50=2\cdot 5^2[/tex]
