There are 150 numbers between 100 and 999 (inclusive) that are divisible by 6.
Calculation and Explanation
The solution is derived using a straightforward method:
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Find the number of multiples of 6 up to 999: We divide 999 by 6: 999 ÷ 6 ≈ 166.5. Since we only consider whole numbers, there are 166 multiples of 6 up to 999.
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Find the number of multiples of 6 up to 99: We divide 99 by 6: 99 ÷ 6 ≈ 16.5. Rounding down, there are 16 multiples of 6 up to 99.
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Subtract to find the numbers between 100 and 999: We subtract the number of multiples of 6 up to 99 from the number of multiples of 6 up to 999: 166 - 16 = 150.
Therefore, there are 150 numbers between 100 and 999 (inclusive) that are divisible by 6. This aligns with the provided reference stating, "Between 1 and 999 there are 999/6 i. e. 166 Numbers that are divisible by 6. Between 1 and 99 there are 99/6 i. e. 16 Numbers that are divisible by 6. Thus between 1 and 999 - 1 and 99 i. e. between 100 and 999 there are 166–16=150 Numbers. Thus 150 is the required answer."
