Alice and Bob are playing the Smallest Positive Integer Game. Alice says, "My number is 24." Bob says, "What kind of silly smallest number is that? Every prime factor of your number is also a prime factor of my number."

Question

What is the smallest possible number that Bob could have? (Remember that Bob's number has to be a positive integer!)

Answer 1

The prime factorization of 24 is 2^3 * 3. The smallest number that has only prime factors that are also prime factors of 24 is the number 2^2 * 3 = 12. Therefore, the smallest possible number that Bob could have is 12.