Numbers Divisible by 7 Between 1000 and 3000
This solution finds the count of numbers strictly between 1000 and 3000 that are divisible by 7.
Finding the Count of Multiples
We can find the total count of numbers divisible by 7 up to 3000 and subtract the count of numbers divisible by 7 up to 999 (the number just before 1000).
- Step 1: Count multiples up to 3000
Divide 3000 by 7 and take the floor of the result.
Number of multiples $\le 3000$ = $\lfloor \frac{3000}{7} \rfloor$
$\lfloor 428.571... \rfloor = 428$ - Step 2: Count multiples up to 999
Divide 999 by 7 and take the floor of the result.
Number of multiples $\le 999$ = $\lfloor \frac{999}{7} \rfloor$
$\lfloor 142.714... \rfloor = 142$ - Step 3: Calculate the difference
Subtract the count from Step 2 from the count in Step 1 to get the numbers in the desired range.
Count = (Multiples $\le 3000$) - (Multiples $\le 999$)
Count = $428 - 142 = 286$
Therefore, there are 286 numbers between 1000 and 3000 that are completely divisible by 7.
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