The digits in the ones place of even numbers are: 

2, 4, 6, 8, 0, 2, 4, 6, 8, 0,....

We notice that the following 5 digits repeat: 2,4,6,8,0

1st even number ends on: 2

2nd even number ends on: 4

3rd even number ends on: 6

4th even number ends on: 8

5th even number ends on: 0

6th even number ends on: 2

.....

We need to find the reminder when 357 is divided by 5.

For the 357th even number we have:

357 = 5*71 + 2

Meaning the ones place will be '4'.

Indeed the 357 even number is: 357*2 = 714