Problem Solving

How many zeros does 135^19 x 42^17 end with?

(a) 0
(b) 2
(c) 5
(d) 13
(e) 17

The OA is the option E.

How can I find the number of zeros fast? I want your explanation experts. Please.

To have a zero at the end, a number must be multiplied by 10. Another way to think of this is that the number must be multiplied by the prime factors 5 and 2.

135 can be factored into 5 and 27. There are no other factors of 5 or 2.
42 can be factored into 2 and 21. There are no other factors of 5 or 2.

So 135^19 will have 19 5s, and 42^17 will have 17 2s. So the answer will end in 17 zeros because there are more 2s than 5s.