How many numbers are divisible by 4 between 1 to 100

Concept: The count of positive integers divisible by d in the inclusive range 1 to N equals floor(N/d). When a range is stated as strictly “between” two numbers, both endpoints are excluded, so any endpoint that happens to itself be a multiple of d must be subtracted from that count.

Application:

1. Multiples of 4 from 1 to 100 inclusive number floor(100/4) = 25, i.e. 4, 8, …, 100.

2. The range is stated as strictly between 1 and 100, so both endpoints are excluded.

3. 100 is itself a multiple of 4, so it must be subtracted: 25 − 1 = 24.

4. 1 is not a multiple of 4, so no further adjustment is needed.

Cross-check: Listing directly, 4, 8, 12, …, 96 is an arithmetic sequence with first term 4, last term 96, and common difference 4; the number of terms = (96 − 4)/4 + 1 = 24, confirming the result.