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There are 3 cases:
An even number time an even number such as 2*6=12 is always even. Proof: Since even numbers can be expressed as 2*X and 2*Y, their product is 4xy which is even.
An even number times an odd number (same as odd times even) such as 2*3=6 is always even. Proof: 2X represents an even number and 2Y+1 represents an odd number. Their product is 4XY+2X=2(2XY+X), which is even.
An odd number times an odd number such as 11*11=121 is always odd. Proof: Let 2X+1 and 2Y+1 be the two odd numbers. Their product is 4XY+2X+2Y+1 = 2(2XY+X+Y)+1, which is odd.
Summary: the product of two numbers is always even unless the two numbers are both odd.
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∙ 11y ago
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Is the product of two odd numbers odd or even?
The product of two odd numbers is always odd.
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.
Can product of 2 odd no be even?
The product of two odd numbers is never even.
What are two odd numbers that make the product of an even number?
No such numbers exist; the product of two odd numbers is always odd.
Can you tell if the product of several numbers will be even or odd?
Yes it is possible to determine if a product will be even or odd. To do this, we need to consider what an even number is. Even numbers are numbers with at least one factor of 2 (meaning they are divisible by 2). Thus, any product of numbers which contains at least one even number will result in an even product. If all of the numbers being multiplied together are odd, the product will be odd. If one or more of the numbers is even, the product will be even.
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.
What is the result of product of even numbers and odd numbers?
If you multiply one even number by one odd number, the result is always even. In general, if you multiply several numbers, and at least one of the numbers is even, the product is always even. This is because "even" means "multiple of 2", and if one of the factors contains a 2 as a factor, so will the product.
How would you describe the rule for determining whether the product of many natural numbers is even or odd?
I would describe the rule as one of the simplest possible.The product is odd only if each of the natural numbers is odd. If any one of them is even, the product is even.I would describe the rule as one of the simplest possible.The product is odd only if each of the natural numbers is odd. If any one of them is even, the product is even.I would describe the rule as one of the simplest possible.The product is odd only if each of the natural numbers is odd. If any one of them is even, the product is even.I would describe the rule as one of the simplest possible.The product is odd only if each of the natural numbers is odd. If any one of them is even, the product is even.
Which pair of numbers has an even product and an odd sum?
Any pair of one even and one odd number will have an even product and an odd sum.
Is the product of two odd numbers even?
no
Is the product of 2 consecutive numbers odd or even?
even
How would you determine whether the product of many natural numbers is even or odd?
If at least one of the numbers is even, the result will be even. Otherwise all the numbers are odd and the result will be odd.
