Question

Every positive integer > 0 can be expressed as a product of
${2}^{n}$
(n ≥ 0) and another ____ (A.) Even no. (B) Odd no. (C) Prime no. (D) both Even & Prime no. ​

Answer 1

Answer:

Every positive integer (greater than 1) can be expressed as product of 2^n (n≥0) and another Odd Number.

The Answer is therefore Option (B)

Step-by-step explanation:

Simple Proof:

Let I be an Integer

If I is an even positive integer  then it will necessarily be divisible by 2 and it can be written as any positive power of 2 multiplied by some odd number

If I is an odd positive integer then it wouldnt be divisible by 2, in this case it can be written as $2^0 \times \text{I}$

Therefore every positive integer greater than  can be written as product of $2^n$ and an odd number.

Hope this helps