Question

5. Using Euclid's division lemma, if the cube of any positive integer is divided by a then the possible remainders are a) 0.1,8 b) 1.4.8 c) 0, 1.3 d) 1, 3, 5​

Answer 1

Answer:

(1) 0, 1, 8 Let the +ve integer be 1, 2, 3, 4 … 13 = 1 when it is divided by 9 the remainder is 1. 23 = 8 when it is divided by 9 the remainder is 8. 33 = 27 when it is divided by 9 the remainder is 0. 43 = 64 when it is divided by 9 the remainder is 1. 53 = 125 when it is divided by 9 the remainder is 8. The remainder 0, 1, 8 is repeated.