What is the number of integers in the range 250 to 750 that are co-prime to 300 ?

The number of numbers co-prime to 300 can be found out by factorizing 300. 300 contains 3 prime factors 2,3,5.
Number of numbers between 250 and 750 divisible by 2 = 251
Number of numbers between 250 and 750 divisible by 3 = 167
Number of numbers between 250 and 750 divisible by 5 = 101
Number of numbers between 250 and 750 divisible by 6 = 84
Number of numbers between 250 and 750 divisible by 10 = 51
Number of numbers between 250 and 750 divisible by 15 = 34
Number of numbers between 250 and 750 divisible by 30 = 17
Required numbers = 501- [251+167+101-(81+51+34)+17] = 131