There are 15,000 five-digit numbers that are divisible by 6.
To determine the number of 5-digit numbers divisible by 6, we need to understand the divisibility rules for 6. A number is divisible by 6 if it's divisible by both 2 and 3.
Here's how we can approach the calculation:
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Identify the range: The smallest 5-digit number is 10,000, and the largest is 99,999.
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Find the first divisible number: The first 5-digit number divisible by 6 is 10,002 (since it's even and 1+0+0+0+2=3, which is divisible by 3).
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Find the last divisible number: The largest 5-digit number divisible by 6 is 99,996 (since it's even and 9+9+9+9+6=42, which is divisible by 3).
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Create an arithmetic sequence: We now have an arithmetic sequence of numbers divisible by 6: 10002, 10008, 10014... 99996. Each number in the sequence is 6 more than the previous. The sequence can be expressed as 6n, where n is an integer.
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Calculate the number of terms:
- We can express the first term (10002) as 6 1667, and the last term (99996) as 6 16666.
- Thus, we need to calculate the difference between the multipliers (16666 - 1667 + 1).
- So the number of terms is 16666 - 1667 + 1 = 15000.
Therefore, there are 15,000 five-digit numbers divisible by 6.
It is important to note that, this method assumes that you are not referencing the information from the reference provided. The reference provides some example data that is not needed to complete this calculation. The calculation of 24+36+48 = 108 (from the reference) appears to be unrelated to this problem.
