A positive integer N divides 228, leaving a remainder of 18. What is the greatest two-digit value of N?
70
N divides 228 leaving remainder 18, so N must divide \(228-18=210\) exactly, and N must exceed 18.
Two-digit divisors of 210: 10, 14, 15, 21, 30, 35, 42, 70.
The greatest two-digit divisor is 70.
Hence, the greatest two-digit value of N is 70.
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