To find the prime factorization of a number, start by having a list of the first several primes in ascending order: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29
Now divide your number by the smallest prime that your number is divisible by and keep dividing by that number until it is no longer divisible. Then move on to the next prime. Keep going until you get 1. That will give you all the prime factors.
81 is odd, so it is not divisible by 2.
Move on to 3.
81/3 = 27
27/3 = 9
9/3 = 3
3/3 = 1
Since we got to 1, we stop.
We divided by 3, 3, 3, 3, so 81 = 3 * 3 * 3 * 3
81m = 3^4 * m