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How many numbers less than 200 are divisible by 7?

Published in Math Problem Solving 1 min read

There are 28 numbers less than 200 that are divisible by 7.

According to the provided reference, there are 28 numbers divisible by 7 between 3 and 200. Since the question asks for numbers less than 200 and all numbers divisible by 7 are greater than 0, we need to find the first multiple of 7 that is within the required range. The first multiple of 7 is 7 (7 x 1) and the multiples increase by 7 each time (7, 14, 21, ...). To confirm the count, we can calculate the largest multiple of 7 less than 200:

  • Divide 200 by 7: 200 / 7 ≈ 28.57
  • Take the integer part: 28
  • Multiply by 7: 28 * 7 = 196

This means that 196 is the largest multiple of 7 that is less than 200. Therefore, the multiples of 7 that are less than 200 are:

  • 7 x 1 = 7
  • 7 x 2 = 14
  • 7 x 3 = 21
    ...
  • 7 x 28 = 196

So, there are 28 multiples of 7 less than 200.

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