The prime factorization of 240 is 2 x 2 x 2 x 2 x 3 x 5
The easy way I was taught how to find the product of primes is: Draw a vertical line. On the left write your number. On the right, write the smallest Prime number that is a factor of this number (i.e ask, does it divide by 2? If the answer is no, then ask does it divide by 3, 5, 7 etc etc until you find a number that does). Then divide the number on the left by the number on the right and write it under the number on the left. Repeat this process until the number on the left is equal to the number on the right (i.e. a prime number).
eg, for 240:
240 | 2
120 | 2
60 | 2
30 | 2
15 | 3
5 | 5