The prime factoization of 2006 is as follow:
The first prime number is 2:
Therefore 2 is a prime factor, now the quotient is 1003 which is not an even number, so 2 is not useful and we must switch to the next prime factor i.e. 3, but 1003 is not a multiple of 3. ...
The prime factorizations of 2006 and 2007 are found by hand.