Find the quotient and the remainder when each of the following numbers is divided by 13.

8, 31, 44, 85, 1220.

We know If s → (q, r) denotes the quotient q and r denotes the remainder r

Then s = (b × q) + r where s and b > 0 and 0 ≤ r < b

When s is divided by 13 then

(i) s = 8

⇒ 8 = 13 × 0 + 8

Here quotient = 0 and r = 8

(ii) s = 31

⇒ 31 = 13 × 2 + 5

Here quotient = 2 and r = 5

(iii) s = 44

⇒ 44 = 13 × 3 + 5

Here quotient = 3 and r = 5

(iv) s= 85

⇒ 85 = 13 × 6 + 7

quotient = 6 and r = 7

(v) s = 1220

⇒ 1220 = 13 × 93 + 11

Here quotient = 93 and remainder = 11