I wrote this to solve another Project Euler problem (the number of divisors for a given triangular number). To find the number of divisors that a number has, the quickest way is to take the prime factorization of the number. Next, add one to each of the exponents of the prime factors, and find the product of these new exponents. There's your num…

trianglenumdivisors.rb

whichtrinum = 1
while true
  trinum = (whichtrinum * (whichtrinum + 1)) / 2
  numtofactor = trinum
	factors = []
	factor = 2
	while numtofactor != 1
		if numtofactor % factor == 0
			factors << factor
			numtofactor = numtofactor / factor
			factor = 2
		elsif factor > Math.sqrt(numtofactor)
			factors << numtofactor
			numtofactor = 1
			factor = 2
		else
			factor.even? ? factor += 1 : factor += 2
		end
	end
	
	divisors = 1
	factors.uniq.each { |base| divisors *= (factors.count(base) + 1) }
	if divisors > 500
		break
	end
	whichtrinum += 1
end

puts trinum

Might have been even more efficient to find the divisors of whichtrinum and (whichtrinum + 1)/2 (or the reverse, depending on which is even) and then multiply together the number of divisors of each... Oh, well, live and learn.