Final answer:
There are 900 integers between 100 and 999 inclusive. When calculating the number of these that are not divisible by 4, we find there are 225 divisible by 4 within this range, and therefore, 675 that are not divisible by 4.
Step-by-step explanation:
To determine how many integers between 100 and 999 inclusive are not divisible by 4, we first need to identify how many numbers there are in total and then exclude those that are divisible by 4. The total count of integers from 100 to 999 is 900 because 999 - 100 + 1 = 900. To find the number of integers divisible by 4 in this range, we observe that the first number divisible by 4 within the range is 100 (since 4 divides into 100 exactly 25 times), and the last is 996 (which is 4 times 249).
The formula to calculate the number of multiples of 4 between two numbers ('a' being the lower bound and 'b' being the upper bound) is given by: NumberOfMultiples = (b/4) - ((a-1)/4). So the count of numbers divisible by 4 between 100 and 999 is (996/4) - (99/4) = 249 - 24 = 225. After finding the count of numbers that are divisible by 4, we subtract this from the total number of integers in our range to get the count of numbers that are not divisible by 4. Therefore, the number of integers not divisible by 4 is 900 - 225 = 675. Hence, 675 integers between 100 and 999 are not divisible by 4.