How many three-digit numbers are divisible by 5 ?

Answer

To find out how many three-digit numbers are divisible by 5, we can follow these steps:

### Step 1: Identify the Range of Three-Digit Numbers
The smallest three-digit number is 100, and the largest three-digit number is 999.

### Step 2: Determine the First Three-Digit Number Divisible by 5
The first three-digit number is 100, and since 100 is divisible by 5 (100 ÷ 5 = 20), we can start from 100.

### Step 3: Determine the Last Three-Digit Number Divisible by 5
The largest three-digit number is 999. To find the largest three-digit number that is divisible by 5, we can check the number just below 999. The largest number less than or equal to 999 that is divisible by 5 is 995 (since 995 ÷ 5 = 199).

### Step 4: Formulate the Arithmetic Progression
Now we have an arithmetic progression (AP) where:
- The first term (a) = 100
- The last term (l) = 995
- The common difference (d) = 5

### Step 5: Use the Formula for the n-th Term of an AP
The n-th term of an AP can be calculated using the formula:
\[ l = a + (n - 1) \cdot d \]
Substituting the known values:
\[ 995 = 100 + (n - 1) \cdot 5 \]

### Step 6: Solve for n
Rearranging the equation:
\[ 995 - 100 = (n - 1) \cdot 5 \]
\[ 895 = (n - 1) \cdot 5 \]
Now, divide both sides by 5:
\[ n - 1 = \frac{895}{5} \]
\[ n - 1 = 179 \]
Now, add 1 to both sides:
\[ n = 180 \]

### Conclusion
Thus, the total number of three-digit numbers that are divisible by 5 is **180**.

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