Question

Given the numbers 2, 4, 8, 10, 14 and 16 : a % b is defined as the remainder when the ordinary product a • b is divided by 18. Find the % product of every pair of these numbers including the product of a number with itself. Fill in the table given below.

(1) Find 2%2%2%....%2, where we find the % product of fifteen 2’s.

(2) Find 8%8%8%.....%8 where we have ten 8’s

Answer 1

2%4 = 8

2%8 = 16

2%10 = 2

2%14 = 10

2%16 = 14

4%8 = 14

4%10 = 4

4%14 = 2

4%16 = 10

8%10 = 8

8%14 = 4

8%16 = 2

10 %14 = 14

10 %16 = 16

14%16 = 8

2%2 = 4

4 % 4 = 16

8 % 8 = 10

10%10 = 10

14%14 = 16

16%16 = 4

(i) 2%2%2%2............2%2

2%2 = 4

4%2 = 8

8%2 = 16

16%2 = 14

14%2 = 10

10%2 = 2

2%2 = 4

Repeated

So, ans = 8.

(ii) 8% 8% 8 % 8......

8% 8 = 10

10% 8 = 8

8 % 8 = 10

% product of ten 8’s = 10.