Question 2: Find a natural number less than 200, knowing that the number divided by 2 has a remainder of 1, a remainder of 1 when divided by 3, a remainder of 1 when divided by 5, and divisible by 7.

Let m be the natural number to be found.

* We have: m divided by 2 leaves a remainder of 1, so m has an odd last digit

m divided by 5 lacks 1, so m ends in 4 or 9

So m has a digit ending in 9.

* m is divisible by 7 so m is a multiple of 7 that ends in 9

We have: 7 . 7 = 49

7. 17 = 119

7. 27 = 189

7. 37 = 259 (Discard because a < 200)

Of the numbers 49, 119, and 189, only 49 leaves a remainder of 1 . when divided by 3

So the number to find is 49

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