Write whether every positive integer can be of the form 4q + 2, where q is an integer. Justify your answer
Solution:
No.
Euclid’s Division Lemma(lemma is similar to a theorem) says that, for given two positive integers, 'a' and 'b', there exist unique integers, 'q' and 'r', such that, b = aq + r, 0 ≤ r < a
We know that
dividend = divisor × quotient + remainder
b is any positive integer
a = 4
b = 4q + r for 0 ≤ r < 4
Where r = 0, 1, 2, or 3
Therefore, every positive integer can be of the form 4q, 4q + 1, 4q + 2 or 4q + 3
✦ Try This: The cube of a positive integer is divided by 9. Using Euclid's division lemma, find what can be the possible remainder?
☛ Also Check: NCERT Solutions for Class 10 Maths Chapter 1
NCERT Exemplar Class 10 Maths Exercise 1.2 Problem 1
Write whether every positive integer can be of the form 4q + 2, where q is an integer. Justify your answer
Summary:
No, every positive integer cannot be of the form 4q + 2, where q is an integer
☛ Related Questions:
- “The product of two consecutive positive integers is divisible by 2”. Is this statement true or fals . . . .
- “The product of three consecutive positive integers is divisible by 6”. Is this statement true or fa . . . .
- Write whether the square of any positive integer can be of the form 3m + 2, where m is a natural num . . . .
visual curriculum