There are 15 integers between 700 and 800 that are completely divisible by 7.
Understanding Divisibility
Divisibility refers to whether a number can be divided by another number without leaving a remainder. In this case, we're looking for integers between 700 and 800 that are perfectly divisible by 7.
Finding the Solution
To find the answer, we can use a systematic approach:
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Find the first number: The smallest integer greater than or equal to 700 that is divisible by 7 is 700 itself. However, we want the first integer after 700 divisible by 7. 700 divided by 7 is approximately 100, so we need to find the next multiple of 7. This is 707 (7 x 101).
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Find the last number: The largest integer less than or equal to 800 that is divisible by 7 is 798 (7 x 114).
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Calculate the total: The number of integers divisible by 7 between 707 and 798 can be calculated by finding the difference between the quotients and adding 1: (114 - 101) + 1 = 14. However, this calculation omits 700 itself. Adding this omitted number results in 14 + 1 = 15 integers.
Different sources provide slightly varying answers, likely due to different interpretations of the question's inclusiveness regarding the boundaries (700 and 800). Some answers suggest 14, while others state 15. The more precise answer, inclusive of 700, is 15.
Example: 707, 714, 721, ..., 798 are all divisible by 7.
References and Discrepancies
Several online resources address this question, but some discrepancies exist in the final answers:
- Some sources correctly identify 15 integers. This Quora answer states 15.
- Other sources provide the answer as 14. This is likely due to an exclusion of 700.
- The variation in answers highlights the importance of clearly defining the boundaries when posing such mathematical questions.
