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Question 760084: The greatest number that always divides the difference between a three digit number and the number formed by reversing its digits is?
Answer by DrBeeee(684)   (Show Source):
You can put this solution on YOUR website! Let A = the number be abc
Let B = the reverse cba
Now write he value of each number
(1) A = 100*a + 10*b + c and
(2) B = 100*c + 10*b + a
Now get the differnce, D,
(3) D = 100*a + 10*b + c - 100*c - 10*b - a or
(4) D = 100*(a - c) + (c - a) or
(5) D = 100*(a - c) - (a - c) or
(6) D = 99*(a - c)
Answer: The greatest number that divides the difference of a 3 digit number and its reverse is 99.
Try it on 764 - 467 = 297 = 99*3
or 321 - 123 = 198 = 99*2 or ....
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