Trying to solve for the largest prime factor without recursion - Ruby

I came across a website called Project Euler and everything was going well until I hit the 3rd problem - The Largest Prime Factor. I don't want to use recursion to solve it. I saw solutions online where they use Math.sqrt and I don't want to use that either. Stubborn, I know.

I'd like to solve it with just loops and if statements. I assumed the input is an odd number. Here is my code. The output keeps coming out as [3] if num = 99 and I can't figure out why. I tried putting a puts statement everywhere to see what was being outputted at each step. One issue I realized was that that the array#p was not resetting after each loop. I tried array.clear but that wasn't much help. Could someone point me in the right direction? Is there some fundamental aspect about arrays, loops, and if-statements that I'm not getting?

def prime(num)
    arr = []
    p = []
    not_p = []
    # first I find all the numbers that num is divisible by
    for i in (2..num/2) 
        if num % i == 0
             arr << i
        end
    end # this should output [3, 9, 11, 33]

    arr.each do |x| #  I loop through each element in the above array
        for i in (2..(x/2)) # I divide each element - x -  by 2 because it cannot be divisble by anything greater than its half
            if x % i == 0 # if x is divisble by i
                not_p << i # I push the i into array#not_p
            end # keep looping until i reaches x/2
        end
        if not_p.length == 0 # if there are no values in array#not_p, then I know x is a prime factor
            p << x # so I push x into array#p
        end  
    end
    return p[-1] # returns the last element of the array, which is the largest
end

puts prime(99)