b) one factor can be oddExplanation:If a NUMBER is a product of two NUMBERS, then the following three CASES are possible:The number is a product of One odd and One even numberTwo even numbersTwo odd numberslet US examine all three cases one by one:Product of one odd and one even number.An odd number is in the form = 2n + 1An even number is in the form = 2nTheir product:⟹ 2n( 2n + 1 )⟹ 4n² + 2n⟹ 2( 2n² + n )We can see, their product can be return the form 2 × k, this is shows it is a multiple of 2, thus product of one odd and one even number is an even number.Product of two even numbers. Let first even number = 2nLet the second even number = 2mTheir product:⟹ 2n × 2m⟹ 4mn⟹ 2( 2mn )We can see, their product can be return the form 2 × k, this is shows it is a multiple of 2, thus product of two even number is an even number.Product of two odd numbers:let the first odd number = 2n + 1let the second odd number = 2m + 1Their product:⟹ 2n + 1 ( 2m + 1 )⟹ 2n( 2m + 1 ) + 1( 2m + 1 )⟹ 4mn + 2n + 2m + 1⟹ 2( mn + n + m ) + 1We can see, 2( mn + n + m ) is an even number as it is in the form 2 × k, but there is a "1" added to an even number. So, the product of two odd number is an odd number. We've seen that for the product of two number to be even, the both 2 number does not have to be even. Even if the one number is odd, then the product can result to an even number too. So, option b) one factor can be odd is the CORRECT option.