how many integers 2 to 90 both inclusive cannot be written as a.b where a and b have no common factors and neither a nor b is equal to 1

The question is asking for the number of integers between 2 and 90 (inclusive) that cannot be expressed as the product of two integers (a and b) that have no common factors (other than 1) and where neither a nor b is equal to 1.

This is essentially asking for the number of prime numbers between 2 and 90, as prime numbers are only divisible by 1 and themselves.

The prime numbers between 2 and 90 are: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89.

So, there are 24 integers between 2 and 90 that cannot be expressed as the product of two integers with no common factors other than 1.