 Quandaries and Queries Who is asking: Student Level: Middle Question: One of my math exercises asks: " Use pairs of prime numbers to find all the numbers less than 50 that have only two prime factors. Make an organized list." I understand prime and composites but just don't understand this question. Please help. Thank you. Nikolas Hi Nikolas, I started a list of primes to see what they can be. I got 2,3,5,7,11,13,17,19,23 The next smallest prime is 29 and the smallest product of 29 with another prime is 2 29 which is larger than 50. Start with 2. What products of 2 with one other prime give a number less than 50? 2 3, 2 5, 2 7, 2 11, 2 13, 2 17, 2 19, 2 23 What product of two 2's with one other prime give a number less than 50? 2 2 3, 2 2 5, 2 2 7, 2 2 11 What product of three 2's with one other prime give a number less than 50? 2 2 2 3, 2 2 2 5 What product of four 2's with one other prime give a number less than 50? 2 2 2 2 3 This is the entire list of numbers less than 50 that have two prime factors, one of which is 2. Next try 3. What products of 3 with one other prime larger than 3 give a number less than 50? 3 5, ... Can you complete the list? Penny Go to Math Central