The largest four-digit number which when divided by 10, 11 and 8 leaves remainder 7 in each case is:
9687
The required number is of the form \(\text{LCM}(10, 11, 8) \times k + 7\) for some integer \(k\).
\(\text{LCM}(10, 11, 8) = 440\).
The largest four-digit multiple of 440 is \(440 \times 22 = 9680\) (since \(440 \times 23 = 10120\) exceeds four digits).
Adding the remainder: \(9680 + 7 = 9687\).
Hence, the largest four-digit number satisfying the condition is 9687.
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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:
