The problem asks us to find the smallest number, let's call it \(x\), that can be added to 56789 to make the sum divisible by 345. After finding \(x\), we need to calculate the sum of its digits.
Finding the Remainder
First, we divide 56789 by 345 to find the remainder.
Using division: \(56789 \div 345\)
\(56789 = 345 \times 164 + 209\)
The remainder when 56789 is divided by 345 is 209.
Calculating the Smallest Number to Add (x)
To make the number 56789 divisible by 345, we need to add a number that completes the next multiple of 345. The current remainder is 209. The amount needed to reach the next multiple of 345 is calculated as:
\(x = \text{Divisor} - \text{Remainder}\)
\(x = 345 - 209\)
\(x = 136\)
So, the smallest number \(x\) that can be added is 136.
Sum of Digits of x
Finally, we need to find the sum of the digits of \(x\).
\(x = 136\)
Sum of digits = \(1 + 3 + 6 = 10\).
Conclusion
The sum of the digits of \(x\) is 10.
Similar Questions
- Find the four-digit dividend of 21, 42, 147 and 105 that will give the remainder 14, 35, 140 and 98, respectively.
- The smallest number that can be added to 56789 to make it divisible by 345 is x. What is the sum of the digits of x?
- If x is the greatest 4-digit number that is divisible by 237, then the sum of digits of x is:
- For which value of k number 345k6 is divisible by 3
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:
