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249-yes, 5-no (Posted on 2019-07-08) Difficulty: 2 of 5
What is the largest 7-digit number that is divisible by 249, but not divisible by 5?

See The Solution Submitted by Ady TZIDON    
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Solution solution Comment 1 of 1
249 = 3 * 83 and is thus relatively prime to 5. Their product, and therefore LCM, is 1245.

9999999/1245 is 8032 with a remainder of 159.

1245 * 8032 = 9999840

Thus 9999840 is a multiple of both 249 and 5. Both adding and subtracting 249 to or from this number will produce a multiple of 249 that's not a multiple of 5.  The addition would give a number with more than 7 digits, so the answer sought results from a subtraction of 249, being 9999591.


  Posted by Charlie on 2019-07-08 14:39:41
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