Question

In euclid division lemma,if a =3q+r,then write all the possible value of r.
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Answer 1

Answer:

r=0,r=1,r=2 these are the value of r,if r=0,a=3q. r=1, a=3q+1.r=2,3q+2

Answer 2

Euclid division lemma states that, For every positive natural numbers a, b , We can define a unique pair of natural numbers q, r such that

a = bq + r and 0 ≤ r < b

Now, We are given that,

In Euclid division lemma, It is stated that,

$\: \: \: \: \: \: \: \: \: \: \: \: \boxed{ \boxed{a = 3q + r}}$

We can clearly observe that, b = 3.

From the above stated relation,

We have :

0 ≤ r < b

0 ≤ r < 3

In words, You could say that, r should be a natural number which is less than 3, but greater than or equal to 0.

There exists 3 such values, 0, 1, 2.

Hence, Required values of r are { 0, 1, 2}