var ans := ""

fcn prime (n : int) : boolean
    if n = 2 then
        result true
    end if
    for s : 2 .. n - 1
        if n mod s = 0 then
            result false
        end if
    end for
    result true
end prime

proc sol (c : int, n : int)
    var check : int
    if c > n then
        return
    end if
    if n mod c = 0 then
        if prime (c) then
            check := n div c
            if check = 1 then
                put intstr (c) ..
                return
            elsif check = 2 then
                put intstr (c) + "*" ..
                return
            else
                put intstr (c) + "*" ..
                if check mod c = 0 then
                    sol (c, check)
                else
                    sol (c + 1, check)
                end if
            end if
            check := 0
        end if
    else
        sol (c + 1, n)
    end if
end sol
for x : 1 .. 5
    sol (2, Rand.Int (2, 3000))
    put ""
end for
put ""
% sol (2, 714768071)

var ans := ""

fcn prime (n : int) : boolean %Straightforward function, checks whether the function is prime or not
    if n = 2 then
        result true
    end if
    for s : 2 .. n - 1
        if n mod s = 0 then
            result false
        end if
    end for
    result true
end prime

proc sol (c : int, n : int) %C = divisor, n = number
    var check : int
    if c > n then %if divisor greater than the number(self explainatory math lol)
        return
    end if
    if n mod c = 0 then %If the divisor divides perfectly into n then
        if prime (c) then %Also if the number is prime factor then
            check := n div c %Check is num/divisor
            if check = 1 then %Say n is 5, divisor is 5, so 5 is a prime factor of 5 and we want the program to return now
                put intstr (c) ..
                return
            else
                put intstr (c) + "*" .. %or if check is > 1 (cant be less)
                if check mod c = 0 then %now if check/divisor is perfect number then (ex: prime factors of 100 :
                %2*2*5*5, you see the 2 repeating? So when we get 2 as a prime factor, 100/2=50, 50 is also divisble by 2!
                %so we needn't go to check 3 right now. have to check with 2 again!
                    sol (c, check) %n is check instead of n, otherwise we would have 2 as a prime factor and the number
                    %will remain 100! So have to make it 50 and make it do the whole thing again.
                else
                    sol (c + 1, check) %If divisor wont repeat then we do this for ex: Prime Factors of 10: 2*5. 10/2 = 5
                    %5 isnt divisible by 2! so we go to 3 now.
                end if
            end if
        end if
    else
        sol (c + 1, n) %if n mod c is not 0 then take the next number
    end if
end sol
for x : 1 .. 5
    sol (2, Rand.Int (2, 12354)) %lol random number prime factors
    put ""
end for
put ""
% sol (2, 714768071)

fcn isPrime (n : int) : boolean
    if n mod 2 = 0 and n ~= 2 then
        result false
    end if
    for i : 3 .. round (sqrt (n)) by 2
        if n mod i = 0 then
            result false
        end if
    end for
    result true
end isPrime

proc primeFactors (n, depth : int)
    put "current depth: ", depth
    var d : int := 2
    loop
        exit when isPrime (n)
        if n mod d = 0 then
            if isPrime (d) then
                put d, " "
                primeFactors (n div d, depth + 1)
                return
            else
                primeFactors (d, depth + 1)
                primeFactors (n div d, depth + 1)
                return
            end if
        else
            d += 1
        end if
    end loop
    put n
end primeFactors

primeFactors (714768071, 1)