prove that the product of two odd number is always an odd number

0 votes
1 view
asked May 19 in Class X Maths by Anmol72540 (15 points)
prove that the product of two odd number is always an odd number.

Please log in or register to answer this question.

1 Answer

0 votes
answered Jun 10 by bhaskarbhar007 Basic (28 points)
We can solve this by Euclid's division lemma.

Let a be any integer and b equal to 2.

Therefore, by Euclid's division lemma remainder will be 0 or 1.

a=2q +0 (for r=0)

a=2q here q is some natural no.

It is divisible by 2. Therefore it is even no.

Or

a= 2q +1 (for r =1)

It is not divisible by 2. Therefore it is addressed no.

Okay a can also be written as 2q-1.

Product of two odd interfere= (2q+1)(2q-1)

                                                    =4q^2-1

As it is not divisible by 2. It will be a odd no.

Hence proved

Related questions

0 votes
1 answer
0 votes
2 answers