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Let me show this to you by an example :

Suppose we wish to multiply 3 and 7. Product or Multiplication by any device is actually carried by the process of addition of 3 seven times, i.e. 3+3+3+3+3+3+3 = 21. Because the two numbers are odd, the result is always odd.

To Summarize, addition of an odd number(i.e. 3) to itself an odd number of times(i.e. 7) always results in an odd number.

The product of an even and an odd number always results in an even number because addition of even number any number of times is always even and an odd number added to itself an even number of times also results in an even number.

For ex. 7*2 = 14, here 7(odd number) is added 2(even number) times, i.e. 7+7=14 which is even.

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Q: Why is the product of two odd numbers odd?
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