441 is odd, so we can't divide it by 2.
Since the sum of its digits is [tex]4+4+1=9[/tex], which is divisible by 3, we can divide 441 by 3, and we have
[tex]441\div 3=147[/tex]
Which is still divisible by 3, because [tex]1+4+7=12[/tex]. We have
[tex]147\div 3=49[/tex]
49 is not divisible by 3 anymore, nor by 5 (it doesn't end with 0 or 5).
It is divisible by 7 though, we have
[tex]49\div 7=7[/tex]
and finally,
[tex]7\div 7=1[/tex]
So, the factorization of 441 is
[tex]441=3^2\times 7^2[/tex]
