There are 24 numbers between 100 and 500 that are divisible by 17.
Determining the Count of Numbers Divisible by 17 Between 100 and 500
To find out how many numbers between 100 and 500 are divisible by 17, we can use the concept of arithmetic progressions (AP). Here's a step-by-step breakdown:
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Identify the first number greater than 100 that's divisible by 17:
- 100 / 17 = 5.88. The next whole number is 6.
- 17 * 6 = 102. Thus, 102 is the first number within the range (100-500) divisible by 17.
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Identify the largest number less than 500 that's divisible by 17:
- 500 / 17 = 29.41. The largest whole number is 29.
- 17 * 29 = 493. Thus, 493 is the last number within the range (100-500) divisible by 17.
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Form the Arithmetic Progression (AP): The numbers divisible by 17 form an AP where:
- First term (a) = 102
- Common difference (d) = 17
- Last term (l) = 493
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Calculate the number of terms (n) in the AP: We use the formula for the nth term of an AP:
- l = a + (n - 1) * d
- 493 = 102 + (n - 1) * 17
- 391 = (n - 1) * 17
- n - 1 = 391 / 17
- n - 1 = 23
- n = 24
Therefore, there are 24 numbers between 100 and 500 that are divisible by 17.
Summary
| Calculation Step | Result |
|---|---|
| First divisible number (a) | 102 |
| Last divisible number (l) | 493 |
| Common difference (d) | 17 |
| Number of terms (n) | 24 |
The reference confirms this result.
The Biggest Number under 500 that's divisible by 17 = 17 * 29 = 493. This is an AP with common difference d = 17, Start term a = 102, Last term l = 493. n = 24. Hence total numbers between 100 and 500 are divisible by 17 = 24.
