Question

If a = 4q + r then what are the conditions for a and q. What are the values<br />
that r can take?

Answer 1

Let "a" be any positive integer.
By Euclid's division lemma, a= bq + r 0 is less than or equal to r less than b.
here, b= 4 , a= 4q + r 0 0 is less than or equal to r less than 4 .
Possible Remainders = 0,1, 2 and 3
hence , a = 4q
a= 4q+1
a= 4q+2
a = 4q +3

Answer 2

Answer:

Let "a" be any positive integer.

By Euclid's division lemma, a= bq + r 0 is less than or equal to r less than b.

here, b= 4 , a= 4q + r 0 0 is less than or equal to r less than 4 .

Possible Remainders = 0,1, 2 and 3

hence , a = 4q

a= 4q+1

a= 4q+2

a = 4q +3

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