Question 11
Number Theory
Level
2
What is the remainder when 359975 is divided by 12?\
The answer is 11.
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Note that 359975+1=359976 is divisible by 4 and 3 because 76 is divisible by 4 and the sum of the digits is 3+5+9+9+7+6 ≅ 5 + 7 + 5 ≅ 0 (mod 3). Therefore, 359976 is divisible by 12, so the remainder when 359975 is divided by 12 is 11.