Three Primes

Weekly Problem 6 - 2010
Can you find three primes such that their product is exactly five times their sum? Do you think you have found all possibilities?
Exploring and noticing Working systematically Conjecturing and generalising Visualising and representing Reasoning, convincing and proving
Being curious Being resourceful Being resilient Being collaborative

Problem



How many sets of three prime numbers have the property that the product of the three numbers is exactly five times their sum? (The order of the three numbers is not important).

If you liked this problem, here is an NRICH task which challenges you to use similar mathematical ideas.