There are 53 numbers between 100 and 1000 that are divisible by 17.
Here's how to determine that:
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Find the first number divisible by 17 that is greater than or equal to 100: Divide 100 by 17, which results in approximately 5.88. Round up to the nearest whole number, which is 6. Multiply 17 by 6: 17 * 6 = 102. So, 102 is the first number in the specified range divisible by 17.
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Find the last number divisible by 17 that is less than or equal to 1000: Divide 1000 by 17, which results in approximately 58.82. Round down to the nearest whole number, which is 58. Multiply 17 by 58: 17 * 58 = 986. So, 986 is the last number in the specified range divisible by 17.
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Determine the total number of multiples: We now know that 17 6 = 102 and 17 58 = 986. Therefore, we need to count the number of multiples of 17 from the 6th multiple to the 58th multiple inclusive. To do this, subtract the smaller multiplier from the larger one and add 1: 58 - 6 + 1 = 53.
Therefore, there are 53 numbers between 100 and 1000 divisible by 17.
