when a positive number n is divided by 7 leaves the remainder 2, when 3n is divided by the same number, then the remainder is

When a positive number nnn is divided by 7 and leaves a remainder 2, we can express this as:
n=7k+2n=7k+2n=7k+2
for some integer kkk. When 3n3n3n is divided by 7, substitute nnn:
3n=3(7k+2)=21k+63n=3(7k+2)=21k+63n=3(7k+2)=21k+6 Since 21k21k21k is divisible by 7, the remainder when 3n3n3n is divided by 7 is the remainder when 6 is divided by 7, which is 6. Thus, the remainder is 6. This matches the standard remainder calculation approach for multiplication in modular arithmetic.