# Write whether every positive integer can be of the form 4q + 2, where q is an integer. Justify your answer.

No

By Euclid’s Lemma,

b = a × q + r, 0 ≤ r < a [Using dividend = divisor × quotient + remainder]

Here, b is any positive integer.

According to the question, a = 4

b = 4q + r where 0 ≤ r < 4

r = 0, 1, 2, 3

So, this must be in the form 4q, 4q + 1, 4q + 2 or 4q + 3.

Hence, every positive integer cannot be of the form 4q + 2.

Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Related Videos
Interactive Quiz:Euclid's Division Lemma44 mins
Fundamental Theorem of Arithmetic-238 mins
Champ Quiz | Fundamental Principle Of Arithmetic41 mins
Euclids Division Lemma49 mins
Fundamental Theorem of Arithmetic- 143 mins
Quiz | Imp Qs on Real Numbers37 mins
NCERT | Imp. Qs. on Rational and Irrational Numbers44 mins
Application of Euclids Division Lemma50 mins
Relation Between LCM , HCF and Numbers46 mins
Quiz | Fun with Fundamental Theorem of Arithmetic51 mins
Try our Mini CourseMaster Important Topics in 7 DaysLearn from IITians, NITians, Doctors & Academic Experts
Dedicated counsellor for each student
24X7 Doubt Resolution
Daily Report Card
Detailed Performance Evaluation
view all courses