A number that is divisible by 6 will be divisible by 2and by 3. An integer is divisible by 2 if its units digit is even. An integer is divisible by 3 if the sum of its digits is divisible by 3.
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The given number has a units digit of 9, which is <em>not even</em>. The number cannot be made divisible by 2 for any inserted digit.