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How many numbers between 100 and 1000 are divisible by 17?
51
53
52
54
To find how many numbers between 100 and 1000 are divisible by 17, follow these steps:
- Identify the range:
- Start from numbers greater than or equal to 100.
- End at numbers less than or equal to 1000.
- Find the smallest number:
- Divide 100 by 17. The quotient is approximately 5.88.
- The smallest integer greater than 5.88 is 6.
- Multiply 6 by 17 to get the first number divisible by 17, which is 102.
- Find the largest number:
- Divide 1000 by 17. The quotient is approximately 58.82.
- The largest integer less than 58.82 is 58.
- Multiply 58 by 17 to get the last number divisible by 17, which is 986.
- Calculate total numbers:
- Subtract the smallest quotient from the largest one: 58 - 6 + 1 = 53
- Conclusion:
- There are 53 numbers between 100 and 1000 divisible by 17.
The correct answer is Option:2 - 53.
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