Prime numbers and divisibility play an important role in this riddle. One of the significant numbers in the riddle has exactly 4 factors – and 2 of those factors are prime numbers.

Another number that fits that description is 35. The factors of 35 are 1, 5, 7, and 35. Notice that the 2 factors in the middle of the sequence of factors (5 and 7) are both prime numbers.

Likewise, the number 15 has 4 factors, which include 1, 3, 5, and 15. Again the 2 factors in the middle of the sequence (3 and 5) are both prime numbers.

Can you identify other numbers which have exactly 4 factors, and in which the middle two numbers in the sequence of factors are both prime?

As an additional exploration, can you identify numbers which have exactly 4 factors, but do not have two prime numbers in the middle of the sequence? Why or why not?

Is it possible that a number could have an odd number of factors, and if so, what would those numbers have in common?

Love riddles involving numbers? Start here with: How many ways can you arrange a deck of cards? and Can you solve the counterfeit coin riddle?

Not the least bit puzzled when solving riddles? TED Ed-has a whole section of riddles! Click here, sit down with your family or friends, and start solving them!