Finish problems 3, 5, and 8

problem03.rb

@@ -0,0 +1,92 @@
+# Algorithm outline:
+# 1) Find all primes below sqrt(number)
+# 2) Remove nonfactors from this list of primes
+# 3) Multiply prime factors together. If they exceed sqrt(number), stop.
+# 4) If not, find another factor to test for primality.
+#    (note that we have found all potential factors in step #1)
+# 5) If not prime, then keep repeating steps #3-4 for each new number
+#    until a prime is found.
+def problem_03(number)
+  prime_list = find_primes_below(Math.sqrt(number).floor)
+  prime_factors = Array.new()
+
+  prime_list.each do |i|
+    if is_factor_of(number, i)
+      prime_factors.push(i)
+    end
+  end
+
+  partial_fact = array_product(prime_factors)
+  while partial_fact <= Math.sqrt(number)
+    remaining_fact = number/partial_fact
+    is_divisible_by = find_divisor(remaining_fact, prime_list)
+    unless is_divisible_by
+      prime_factors.push(remaining_fact)
+    end
+    partial_fact = array_product(prime_factors)
+  end
+
+  return prime_factors.max
+end
+
+# Returns an array of all primes below number, inclusive.
+# Uses Sieve of Eratosthenes algorithm
+def find_primes_below(number)
+	primes = Array.new(number + 1, true)
+  primes[0] = false
+  primes[1] = false
+  prime_count = primes.length - 2
+	index = 2
+	while index < primes.length
+		multiple = 2
+    number_not_prime = index * multiple
+    while number_not_prime < primes.length
+      if primes[number_not_prime] == true
+        primes[number_not_prime] = false
+        prime_count = prime_count - 1
+      end
+      multiple = multiple + 1
+      number_not_prime = index * multiple
+    end
+    index = index + 1
+	end
+
+  # Convert boolean array to integer array
+  prime_integers = Array.new(prime_count, nil)
+  count = 0
+  (0..primes.length).each do |i|
+    if primes[i] == true
+      prime_integers[count] = i
+      count = count + 1
+    end
+  end
+  return prime_integers
+end
+
+def is_factor_of(number, candidate)
+  if number % candidate == 0
+    return true
+  else
+    return false
+  end
+end
+
+# Finds a divisor for number in array. Returns false if no divisor is found.
+def find_divisor(number, array)
+  array.each do |i|
+    if number % i == 0
+      return i
+    end
+  end
+  return false
+end
+
+def array_product(array)
+  product = 1
+  array.each do |i|
+    product = product * i
+  end
+  return product
+end
+
+puts problem_03(600851475143)

problem05.rb

@@ -0,0 +1,53 @@
+# Algorithm outline:
+# 1) Find all primes up to and including number.
+# 2) Set lcm at 1.
+# 3) Multiply lcm by the largest multiple of each prime that remains
+#    below number.
+def problem_05(number)
+  lcm = 1
+  prime_array = find_primes_below(number)
+  prime_array.each do |prime|
+    i = prime
+    while i <= number
+      lcm = lcm * prime
+      i = i * prime
+    end
+  end
+  return lcm
+end
+
+# Returns an array of all primes below number, inclusive.
+# Uses Sieve of Eratosthenes algorithm
+def find_primes_below(number)
+  primes = Array.new(number + 1, true)
+  primes[0] = false
+  primes[1] = false
+  prime_count = primes.length - 2
+  index = 2
+  while index < primes.length
+    multiple = 2
+    number_not_prime = index * multiple
+    while number_not_prime < primes.length
+      if primes[number_not_prime] == true
+        primes[number_not_prime] = false
+        prime_count = prime_count - 1
+      end
+      multiple = multiple + 1
+      number_not_prime = index * multiple
+    end
+    index = index + 1
+  end
+
+  # Convert boolean array to integer array
+  prime_integers = Array.new(prime_count, nil)
+  count = 0
+  (0..primes.length).each do |i|
+    if primes[i] == true
+      prime_integers[count] = i
+      count = count + 1
+    end
+  end
+  return prime_integers
+end
+
+puts problem_05(20)

problem08.rb

@@ -0,0 +1,17 @@
+def problem_08()
+  number = 7316717653133062491922511967442657474235534919493496983520312774506326239578318016984801869478851843858615607891129494954595017379583319528532088055111254069874715852386305071569329096329522744304355766896648950445244523161731856403098711121722383113622298934233803081353362766142828064444866452387493035890729629049156044077239071381051585930796086670172427121883998797908792274921901699720888093776657273330010533678812202354218097512545405947522435258490771167055601360483958644670632441572215539753697817977846174064955149290862569321978468622482839722413756570560574902614079729686524145351004748216637048440319989000889524345065854122758866688116427171479924442928230863465674813919123162824586178664583591245665294765456828489128831426076900422421902267105562632111110937054421750694165896040807198403850962455444362981230987879927244284909188845801561660979191338754992005240636899125607176060588611646710940507754100225698315520005593572972571636269561882670428252483600823257530420752963450
+  # Convert number to string, then to array, then convert array elements to ints
+  number_array = number.to_s.split('').map(&:to_i)
+  max = 0
+  (0..number_array.length-5).each do |i|
+    candidate_product = 1
+    (0..4).each do |j|
+      candidate_product = candidate_product * number_array[i+j]
+    end
+    if candidate_product > max
+      max = candidate_product
+    end
+  end
+  return max
+end
+puts problem_08