If a and b are positive integers such that a/b = 2.14, which of the following must be a divisor of a?
Pick one.
A) 15 B) 12 C) 25 D) 102 E) 107
1) A and B are positive INTEGERS   2) A/B = 2.14   A = 214   B = 100   214/100= 
<gadget id="calculator">214/100</gadget>
<output>107/50 = around 2.14</output>
2.14   These values are NOT the smallest possible values though (since they're both even, we can divide both by 2)...   A= 107   B = 50   107/50= 
<gadget id="calculator">107/50</gadget>
<output>107/50 = around 2.14</output>
2.14   There is no other way to reduce this fraction, so A must be a multiple of 107 and B must be an equivalent multiple of 50. At this point though, the value of B is irrelevant to the question. We're asked for what MUST divide into A....   Since A is a multiple of 107, we have to 'factor-down' 107. This gives us only 107, apart from 1. So this integer MUST be a factor of A. You'll find the match in the answer choices.   Answer: 107
<result>E</result>
If a and b are positive integers such that a/b = 2.14, which of the following must be a divisor of a?