There are 9 natural numbers between 10 and 60 that are divisible by 6.
To find the number of natural numbers between 10 and 60 that are divisible by 6, we can follow these steps:
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Identify the first number divisible by 6 within the range: The first multiple of 6 greater than 10 is 12 (6 x 2).
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Identify the last number divisible by 6 within the range: The last multiple of 6 less than 60 is 54 (6 x 9).
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Determine the sequence of multiples of 6: The numbers are 12, 18, 24, 30, 36, 42, 48, and 54. We can represent this as: 6 x 2, 6 x 3, 6 x 4, 6 x 5, 6 x 6, 6 x 7, 6 x 8, and 6 x 9.
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Calculate the number of terms: The multiples of 6 are 6 x 2 to 6 x 9. To find how many numbers are in this range, subtract the lower multiplier from the upper multiplier and add 1: 9 - 2 + 1 = 8. However, the prompt asked for numbers between 10 and 60, implying neither 10 nor 60 are included. This does not change the sequence used, as the lowest value (12) and the highest value (54) are already determined by the parameters. Thus, this calculation is flawed.
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Correct Calculation: The series is 12, 18, 24, 30, 36, 42, 48, 54. By manually counting these terms or by recognizing the pattern established in Step 3 (6 x 2 through 6 x 9) we see that there are 8 total. Let's fix step four: 9 (as shown in step 2) minus 1 (10/6 rounded up to 2, as show in step 1, but decremented by 1) which equals 9-1 or 8 .
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Therefore, there are 8 natural numbers between 10 and 60 that are divisible by 6.
