There are 90 three-digit even numbers divisible by 5.
Here's how we arrive at that answer:
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Divisibility Rules: A number divisible by 5 must end in 0 or 5. An even number must end in 0, 2, 4, 6, or 8. To satisfy both conditions, the number must end in 0.
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Three-Digit Numbers: Three-digit numbers range from 100 to 999.
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Finding the First Number: The smallest three-digit number divisible by 5 and even is 100.
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Finding the Last Number: The largest three-digit number divisible by 5 and even is 990.
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Listing the Numbers: The numbers we're looking for are 100, 110, 120, ..., 990. This is an arithmetic sequence.
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Calculating the Count: We can find the number of terms in the sequence using the formula:
Number of terms = (Last term - First term) / Common difference + 1In this case:
Number of terms = (990 - 100) / 10 + 1 = 890 / 10 + 1 = 89 + 1 = 90
Therefore, there are 90 three-digit even numbers divisible by 5.
