juanita secret number is a factor of 60.... her second clue is her secret numbers is prime number

First, we have to find all the factors of the number 60
So if the clues are that the number is a factor of 60 and is a prime number, the number of Juanita could be any of these numbers: 2, 3, 5. Because those 3 numbers are factors of 60 and are prime numbers.
Now let's see the first multiples of each number:
So the numbers that have 15 as a multiple are 3 and 5. So until now, the number of Juanita could be any of those two numbers let's see which of them is a factor of 20.
The number 5 is a factor of 20. That means that the number of juanita is 5 because is the only number that meets all the requirements (the clues).