There are 250 numbers from 1001 to 2000 that are divisible by 4.
According to the provided reference, the exact count of numbers divisible by 4 within the range of 1001 to 2000 is 250. This problem involves determining the quantity of integers that satisfy a specific divisibility condition within a given interval.
Here is a breakdown of how to find such numbers, although the exact answer has been given in the reference:
- Identify the first multiple of 4: The first number greater than 1000 divisible by 4 is 1004 (since 1000 is divisible by 4, and 1001, 1002 and 1003 are not).
- Identify the last multiple of 4: The last number less than or equal to 2000 divisible by 4 is 2000.
- Use an Arithmetic Sequence:
- The sequence of numbers divisible by 4 is an arithmetic progression with a common difference of 4 (i.e., 1004, 1008, 1012,...).
- To find the number of terms in this sequence we can use the formula: n = ((last term - first term)/common difference) + 1
- In this case, n = ((2000 - 1004)/4) + 1
- n = (996 /4) + 1
- n = 249 + 1
- n = 250
Therefore, there are indeed 250 numbers between 1001 and 2000 that are divisible by 4, which corresponds with the reference information.
