Solved a few more problems

003: php
005: php, ruby
006: php, ruby, c

ProjectEuler/003/desc.yml

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+title: Find the largest prime factor of a composite number.
+url: http://projecteuler.net/problem=3
+
+desc: |
+  The prime factors of 13195 are 5, 7, 13 and 29.
+  What is the largest prime factor of the number 600851475143 ?
+  
+solution: |
+  Use factorization to find the largest prime factor
+
+solutions:
+  solve.php:
+    desc: Basic solution
+    language: php
+

ProjectEuler/003/solve.php

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+<?php
+$number = 600851475143;
+
+echo max(factorize($number));
+
+/**
+ * Returns a sorted array of the prime factorization of $num
+ * @staticvar array $aFactors
+ * @param type int Number to factorize
+ * @return type array Prime factors
+ */
+function factorize($num) {
+	// Returns a sorted array of the prime factorization of $num 
+	// Caches prior results.  Returns empty array for |$num|<2 
+	// eg. factorize(360) => [5, 3, 3, 2, 2, 2] 
+	static $aFactors = array();
+	if (2 > $num = abs($num))
+		return array();  // negatives, 1, 0 
+
+	if ($aFactors[$key = "x$num"]) {	 // handles doubles 
+		// Been there, done that 
+		if (($factor = $aFactors[$key]) == $num)
+			return array($num);
+		return array_merge(factorize($num / $factor), array($factor));
+	}
+
+	// Find a smallest factor 
+	for ($sqrt = sqrt($num), $factor = 2; $factor <= $sqrt; ++$factor)
+		if (floor($num / $factor) == $num / $factor)
+			return array_merge(factorize($num / $factor), array($aFactors[$key] = $factor));
+
+	return (array($aFactors[$key] = $num));
+}

ProjectEuler/005/desc.yml

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+title: What is the smallest number divisible by each of the numbers 1 to 20?
+url: http://projecteuler.net/problem=5
+
+desc: |
+  2520 is the smallest number that can be divided by each of the numbers from 1 to 10 without any remainder.
+  What is the smallest positive number that is evenly divisible by all of the numbers from 1 to 20?
+  
+solution: |
+  See code
+
+solutions:
+  solve.php:
+    desc: Basic solution
+    language: php
+  solve.rb:
+    desc: Basic solution in Ruby
+    language: ruby

ProjectEuler/005/solve.php

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+<?php
+for($i=20;true;$i+=20) {
+	$div = 19;
+
+	while(!($i % $div)) {
+		$div--;
+		if($div == 0) {
+			echo $i;
+			die;
+		}
+	}
+}

ProjectEuler/005/solve.rb

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+max = 0;
+(100..1000).each do |num1|
+	(100..1000).each do |num2|
+		sum = num1 * num2
+		if( sum > max and sum.to_s.reverse  == sum.to_s) 
+			max = sum
+		end
+	end
+end
+print max

ProjectEuler/006/desc.yml

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+title: What is the smallest number divisible by each of the numbers 1 to 20?
+url: http://projecteuler.net/problem=6
+
+desc: |
+  The sum of the squares of the first ten natural numbers is,
+  1^2 + 2^2 + ... + 10^2 = 385
+  The square of the sum of the first ten natural numbers is,
+  (1 + 2 + ... + 10)^2 = 55^2 = 3025
+  Hence the difference between the sum of the squares of the first ten natural numbers and the square of the sum is 3025  385 = 2640.
+  Find the difference between the sum of the squares of the first one hundred natural numbers and the square of the sum.
+  
+solution: |
+  See code
+
+solutions:
+  solve.php:
+    desc: Basic solution
+    language: php
+  solve.rb:
+    desc: Basic Ruby solution
+    language: ruby
+  solve.rb
+    desc: ANSI C solution (Tested with TCC)
+    language: c

ProjectEuler/006/solve.c

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+#include <stdio.h>
+#include <math.h>
+
+int main( )
+{
+	int num;
+	int result;
+	
+	int square = 0;
+	int sum = 0;
+	
+	for(num=1; num<=100; num++) {
+		square += pow(num,2);
+		sum += num;
+
+	}
+	result = pow(sum,2) - square;
+	printf("%d", result);
+}

ProjectEuler/006/solve.php

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+<?php
+$square =0;
+$sum =0;
+for($num=1;$num<101;$num++) {
+	$square += pow($num,2);
+	$sum += $num;
+
+}
+echo pow($sum,2) - $square;

ProjectEuler/006/solve.rb

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+square = 0
+sum = 0
+(1..100).each do |num| 
+	square += num**2;
+	sum += num;
+end
+puts sum**2 - square;