If you memorize the multiplication table up to 12x12, then you could recognize that 12x12=144, then you only have to factor each of the 12's is 3 x 2 x 2.
So 144 = 2 x 2 x 2 x 2 x 3 x 3. But if you don't know this, then: By inspection, it has 2 as a factor, then by sum of digits, it has 9 as a factor. Start by dividing the number by 2, until you are down to a number that cannot be divided by 2, then start dividing by 3 or 9, until you get to a number that is not divisible by 3 or 9, then see what you have left, and see if that number is prime. In this case, if you divide by 2, four times, then you are left with 9, which is 3 x 3.
Since 72 is a factor of 144, its whole prime factorization will be contained in the prime factorization of 144.
Since 72 is a factor of 144, its entire prime factorization will be contained in the prime factorization of 144.
2 * 2 * 2 * 2 * 3 * 3 = 144
144 72,2 36,2,2 18,2,2,2 9,2,2,2,2 3,3,2,2,2,2
2x2x2x2x3x3
since 144 is 122 you can find the primefactorization easy by noting that 12=22 x3 so 144=24x32
144 = 24 32
The prime factors of 144 are: 2,3
24*32 = 144
144 = 24 x 32
24 x 32 = 144
24 x 32 = 144