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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Important Questions from Divisibility and Remainder
If the 8-digit number 888x53y4 is divisible by 72, then what is the value of (7x + 2y), for the maximum value of y?
If all positive divisors of 132 are arranged in descending order, then what digit will be at unit place of first divisor ?
If 3 2019 is divided by 10, then what is the remainder?
The number 3798125P369 is divisible by 7. What is the value of the digit P?
Consider all 3-digit numbers (without repetition of digits) obtained using three non-zero digits which are multiples of 3. Let S be their sum.
Which of the following is/are correct?
1. S is always divisible by 74.
2. S is always divisible by 9.
select the correct answer using the code given below:
