add problem solutions

problem03.rb

@@ -0,0 +1,19 @@
+#problem 3 largest prime factor
+#break down to primes
+
+def big_factor(num)
+  iter = 2
+  big_prime = 0
+
+  while iter <= num
+    if num % iter == 0
+      while num % iter == 0
+        num = num / iter
+        big_prime = iter
+        iter += 1
+      end
+    end
+    iter += 1
+  end
+  big_prime
+end

problem05.rb

@@ -0,0 +1,12 @@
+#problem 5
+#Euclid algorithms: lcm = (numa * numb)/gcd(numa,numb)
+#					gcd = num_a % num_b until = 0
+
+def great_com_div(num_a, num_b)
+	num_a, num_b = num_b, num_a % num_b
+	num_b == 0 ? num_a : great_com_div(num_a, num_b)
+end
+
+def least_com_mult(limit)
+	(1..limit).inject(1){|a,b| (a*b)/great_com_div(a,b)}
+end

problem08.rb

@@ -0,0 +1,34 @@
+# problem 8
+# I know there is supposed to be some magic math to solve this but cant think of it
+
+number = '73167176531330624919225119674426574742355349194934
+96983520312774506326239578318016984801869478851843
+85861560789112949495459501737958331952853208805511
+12540698747158523863050715693290963295227443043557
+66896648950445244523161731856403098711121722383113
+62229893423380308135336276614282806444486645238749
+30358907296290491560440772390713810515859307960866
+70172427121883998797908792274921901699720888093776
+65727333001053367881220235421809751254540594752243
+52584907711670556013604839586446706324415722155397
+53697817977846174064955149290862569321978468622482
+83972241375657056057490261407972968652414535100474
+82166370484403199890008895243450658541227588666881
+16427171479924442928230863465674813919123162824586
+17866458359124566529476545682848912883142607690042
+24219022671055626321111109370544217506941658960408
+07198403850962455444362981230987879927244284909188
+84580156166097919133875499200524063689912560717606
+05886116467109405077541002256983155200055935729725
+71636269561882670428252483600823257530420752963450'.gsub("\n","")
+
+def hugest_product(number)
+	numbers = number.split("")
+	max=0
+
+	numbers.each_index do |i|
+		product = numbers[i].to_i * numbers[i+1].to_i * numbers[i+2].to_i  * numbers[i+3].to_i * numbers[i+4].to_i 
+		max = product if product > max
+	end
+	max
+end