Largest 4-Digit Number Identification
The greatest number of 4 digits is 9999.
Divisibility Calculation
We need to find the smallest positive number to add to 9999 so that the sum is exactly divisible by 307.
First, divide 9999 by 307 to find the remainder:
$ 9999 \div 307 $
Performing the division:
$ 9999 = 307 \times 32 + 175 $
The remainder is 175.
Number to Add Determination
For the sum $9999 + x$ to be exactly divisible by 307, the remainder 175 needs to be increased to the next multiple of 307. The next multiple of 307 after 9999 is $307 * 33$.
Alternatively, we need $175 + x$ to be the next multiple of 307, which is 307.
Set up the equation:
$ 175 + x = 307 $
Solve for $x$:
$ x = 307 - 175 $
$ x = 132 $
Therefore, the smallest positive number that must be added is 132.
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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:
