There are 90 three-digit numbers that are divisible by both 2 and 5.
A number divisible by both 2 and 5 must be divisible by their least common multiple, which is 10 (2 * 5 = 10). Therefore, we need to find the number of three-digit numbers divisible by 10. Three-digit numbers range from 100 to 999.
Here's how we can calculate this:
- The smallest three-digit number divisible by 10 is 100.
- The largest three-digit number divisible by 10 is 990.
- We can form an arithmetic sequence with a common difference of 10: 100, 110, 120, ..., 990.
To find the total count of these numbers, we can use the formula for the number of terms in an arithmetic sequence:
Number of terms = (Last term - First term) / Common difference + 1
In our case:
Number of terms = (990 - 100) / 10 + 1 = 890 / 10 + 1 = 89 + 1 = 90
Therefore, there are 90 three-digit numbers divisible by both 2 and 5. This aligns with the information from the provided reference, which states that the total number of 3-digit numbers divisible by 2 and 5 is 90.
