There are 67 numbers between 400 and 800 divisible by 6.
Understanding Divisibility
A number is divisible by 6 if it's divisible by both 2 and 3. This means the number must be even and the sum of its digits must be divisible by 3.
Calculating the Number of Multiples
To find the number of multiples of 6 between 400 and 800, we can use the following method:
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Find the smallest multiple: The smallest multiple of 6 greater than or equal to 400 is 402 (400/6 ≈ 66.67, so the next multiple is 67*6 = 402).
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Find the largest multiple: The largest multiple of 6 less than or equal to 800 is 798 (800/6 ≈ 133.33, so the largest multiple is 133*6 = 798).
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Calculate the number of multiples: The number of multiples is found by subtracting the smallest multiple from the largest multiple, dividing by the divisor (6), and adding 1: (798 - 402) / 6 + 1 = 67.
Therefore, there are 67 numbers between 400 and 800 that are divisible by 6. Note that some references provided discuss divisibility by 4, 5, and 6, which yields a different, smaller number of results (7). This question focuses solely on divisibility by 6.
Example Multiples
Here are a few examples of numbers between 400 and 800 divisible by 6:
- 402
- 408
- 414
- ...
- 792
- 798
