The fifth workshop in Dr Joel Feinstein's G11FPM Foundations of Pure Mathematics module covers a worksheet based on applications of the Fundamental Theorem of Arithmetic. Counting the number of different positive factors (divisors) of a positive integer. Divisibility. Highest powers of primes dividing a given positive integer. Another way to prove that certain real numbers are irrational.. These videos are also available for download on iTunes U at: itunes.apple.com/us/itunes-u/foundations-pure-mathematics/id950755120 Dr Feinstein's blog may be viewed at: explainingmaths.wordpress.com. Dr Joel Feinstein is an Associate Professor in Pure Mathematics at the University of Nottingham.