How many prime numbers less than 100 are there that when divided by 5 leaves an odd remainder?

13 numbers

Since we are looking to find odd reminder which implies that the remainder will be either 1 or 3

Therefore number must follow below two conditions:

A) We can list number 5n + 1 or 5n + 3. (where n = 0,1,2,3.....)

B) The number must end in 1 or 3.

List of such numbers less than 100 are:

1, 3, 11, 13, 21, 23, 31, 33, 41, 43, 51, 53, 61, 63, 71, 73, 81, 83, 91, 93

Let us remove the nonprime ones which are 1, 21, 33, 51, 63, 81 and 91

So, I will be left with 13 numbers which fit the bill.

3, 11, 13, 23, 31, 41, 43, 53, 61, 71, 73, 83 and 93