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Here's the following proof that "product of two odd numbers is odd".
Proof: Any odd number can be written in the form 2p+1. Let your first odd number be written in this form. Let your second odd number be written as 2q+1 - essentially the same form as above, but since p may not equal q, separate variables are used.
Thus: First odd number x second odd number = (2p+1)(2q+1)
= 2pq + 2p +2q +1.
The plus one on the end indicates that the product is odd, as required.
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Which pair of numbers has an odd product and an even sum?
Any two odd numbers will have an odd product and an even sum.
What type of number is the product of two odd numbers?
an odd number
Is the product of any two prime numbers is always odd?
No, because 2 is prime. Otherwise the product of two odds is odd, and all primes are odd except 2.
What two consecutive number have a product of 324?
No two consecutive numbers have a product that is an even number. Any two consecutive numbers include one odd number and one even number. The product of one odd number and one even number is always an odd number.
When multiplying an odd number by an odd number why is the result odd?
The product of multiplication results in a number that has all of the factors of the two numbers being multiplied. All even numbers have the prime factor 2. Since no odd number has the factor 2, no product of those numbers can have it. So: - Odd numbers times odd numbers produce odd numbers. - Odd numbers times even numbers produce even numbers. - Even numbers times even numbers produce even numbers.
