On dividing 2272 as well as 875 by 3-digit number N, we get the same remainder. The sum of the digits of N is:10111213
Question
On dividing 2272 as well as 875 by 3-digit number N, we get the same remainder. The sum of the digits of N is:10111213
Solution
The problem is asking for a 3-digit number N that gives the same remainder when both 2272 and 875 are divided by it.
Step 1: We need to find the difference between 2272 and 875, because if two numbers give the same remainder when divided by a number, then their difference is exactly divisible by that number.
2272 - 875 = 1397
Step 2: Now, we know that N is a factor of 1397. We also know that N is a 3-digit number. The factors of 1397 are 1, 3, 7, 9, 21, 27, 51, 63, 81, 93, 189, 243, 279, 567, 837, 1397.
The only 3-digit factors are 567 and 837.
Step 3: We need to find the sum of the digits of these two numbers.
For 567, the sum is 5 + 6 + 7 = 18.
For 837, the sum is 8 + 3 + 7 = 18.
So, the sum of the digits of N is 18.
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