There are 150 three-digit numbers that are completely divisible by 6.
Here's how we can determine that:
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Identify the Range: We need to find the number of multiples of 6 between 100 and 999 (inclusive).
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Find the first three-digit multiple of 6: The smallest three-digit number is 100. Dividing 100 by 6 gives approximately 16.67. So, the first three-digit number divisible by 6 is 17 * 6 = 102.
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Find the last three-digit multiple of 6: The largest three-digit number is 999. Dividing 999 by 6 gives 166.5. So, the last three-digit number divisible by 6 is 166 * 6 = 996.
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Calculate the number of multiples: Now we need to find how many multiples of 6 there are between 102 and 996. We can do this using the following formula:
Number of multiples = (Last multiple - First multiple) / 6 + 1
Number of multiples = (996 - 102) / 6 + 1
Number of multiples = 894 / 6 + 1
Number of multiples = 149 + 1
Number of multiples = 150
Therefore, there are 150 three-digit numbers that are completely divisible by 6.
