Question

19.For any positive integer 'a' and 3, there exist
unique integers 'q' and 'r' such that a = 3q + r
where 'r' must satisfy
a. 0 <r <3
b. 0<r <3
c. 0<r <3
d. 1<r <3​

Answer 1

$\huge \tt{♕︎αɳรωεɾ♕︎}$

→ Euclid’s division Lemma:

→ It tells us about the divisibility of integers. It states that any positive integer ‘a’ can be divided by any other positive integer ‘ b’ in such a way that it leaves a remainder ‘r’.

→ Euclid's division Lemma states that for any two positive integers ‘a’ and ‘b’ there exist two unique whole numbers ‘q’ and ‘r’ such that , a = bq + r, where 0≤ r < b.

→ Here, a= Dividend, b= Divisor, q= quotient and r = Remainder.

→ Given :

→ a=3q+r

→ In this question ,

b=3

→ The values 'r’ can take 0≤r<3.

→ Hence, the possible values 'r’ can take is 0,1,2.