5^100 is divided by 18. Then what is the remainder? Choose the correct choice from the following options.
A) 10
B) 11
C) 13
D) 15
E) 16

Rationale: "here n = 18 = 2 × 32 ϕ ( 18 ) = 18 ( 1 − 12 ) ( 1 − 13 ) = 6 so 56 when divided by 18 , remainder is 1 . so we can write the given expression 5100 = ( 56 ) 16 × 54 = ( 1 ) 16 × 54 = 52 × 52 = 7 × 7 = 49 now 49 when divided by 18 , remainder is 13 . c"
Answer: C