How many numbers between 800 and 2000 are divisible by 13?

There are 92 numbers between 800 and 2000 that are divisible by 13. This conclusion is based on the reference provided.

Here's a breakdown of how to determine this without directly calculating every number:

Find the first multiple of 13 greater than 800:
- Divide 800 by 13, which is approximately 61.54.
- Round up to the next whole number, which is 62.
- Multiply 62 by 13: 62 * 13 = 806. This is the first multiple of 13 within the range.
Find the last multiple of 13 less than 2000:
- Divide 2000 by 13, which is approximately 153.85.
- Round down to the nearest whole number, which is 153.
- Multiply 153 by 13: 153 * 13 = 1989. This is the last multiple of 13 within the range.
Use the Arithmetic Progression Formula to find the count:
- The multiples of 13 form an arithmetic sequence (806, 819, 832, .... 1989)
- To find out how many terms there are in the series, we can use the formula:
- n = ((last term - first term)/common difference) + 1.
- n = ((1989 - 806)/13) + 1
- n = (1183/13) + 1
- n = 91 + 1
- n = 92

Therefore, there are 92 numbers between 800 and 2000 that are divisible by 13.

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