The factors are 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72.I find factors in pairs, It will look like more work than it is, because I will explain how I am doing these steps. I do most of the work without writing it down. Ill put the explanation in black in [brackets] and the answer in $color(blue)blue$.
Ill proceed by starting with $1$ on the left and checking each number in order until either I get to a number already on the right or I get to a number greater than the square root of 72.
$color(blue)(1 xx 72)$
[I see that 72 is divisible by 2, and do the division to get the next pair]
$color(blue)(2 xx 36)$
[Now we check 3 and we get the next pair.]
[I use a little trick for this. I know that 36 is divisible by 3 and $36 = 3xx12$. This tells me that $72 = 2xx3xx12$, so I know that $72 = 3xx2xx12 = 3xx24$]
$color(blue)(3 xx 24)$
[Now we need to check 4. Up above, we got $72 = 2xx36$ since $36 = 2xx18$, we see that $72 = 2xx2xx18 = 4xx18$]
$color(blue)(4 xx 18)$
[The next number to check is 5. But 72 is not divisible by 5. I usually write a number before I check, so if a number is not a factor, I cross it out.]
$color(blue)cancel(5)$
{Move on to 6. Looking above I want to build a 6 by multiplying a number on the left times a factor of the number to its right. I see two ways to do that: $2xx36 = 2xx3xx12 = 6xx12$ and $3xx24 = 3xx2xx12=6xx12$. (Or maybe you just know that $6xx12=72$.)]
$color(blue)(6 xx 12)$
[72 is not divisible by 7.]
$color(blue)cancel(7)$
{$4xx18 = 4xx2xx9=8xx9$]
$color(blue)(8 xx 9)$
[And thats all. 9 and the factors that are greater than 9 are already written on the right in the list of pairs above.]
[Is that clear? Any factor of 72 greater than 9 must be multiplied by something less than 8 to get 72. But weve checked all the numbers up to and including 8. So were finished.]
[If we were doing this for $39$ we would get $1xx39$ and $3xx13$, then we cross off every number until we notice that $7xx7 = 49$. If 39 had a factor greater than 7 it would have to be multiplied by something less that 7 (otherwise we get 49 or more). So we would be finished.]