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:
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:
Solution
To solve this problem, we need to find the difference between 2272 and 875, which is 1397.
The 3-digit number N that divides both 2272 and 875 leaving the same remainder must be a factor of the difference 1397.
The factors of 1397 are 1, 3, 7, 21, 23, 67, 69, 201, 469, 1397.
The only 3-digit factors are 201 and 469.
The sum of the digits of 201 is 2+0+1 = 3.
The sum of the digits of 469 is 4+6+9 = 19.
So, the possible sums of the digits of N are 3 and 19.
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