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# Why is the product of an even number and any other number always even?

Updated: 12/9/2022

Wiki User

11y ago

When you multiply numbers together, the factors of the product are the factors of all of the multiplicands, and every even number includes at least one factor of 2.

Wiki User

11y ago

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Q: Why is the product of an even number and any other number always even?
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### When you multiply any number of even numbers will the product always be odd?

No, the product will always be even.

### Will the product of two consecutive integers be odd or even?

It will alway be even, because it will always be the product of an odd and an even number, which is always even.

### How do you use inductive reasoning to prove the product of an odd integer and an even integer will always be even?

The product of an odd and even number will always have 2 as a factor. Therefore, it will always be even.

yes

### Why is the product of two consecutive numbers is always odd?

When multiplied together, an odd number and an even number will always produce an odd number. Two consecutive numbers consist of one odd number and one even number, so their product is always an odd number. N-n-n-no! Any number multiplied by an even number yields an even product. Ever;y even number can be expressed as 2*M for some M. If we multiply 2*M by Y, the product is 2*M*Y = 2*(M*Y) which is even. So the right answer is: They don't! The product of two consecutive numbers is always even. Regards, Bill Drissel

even

### When a whole number is multiplied by 4 the product will always be an even number?

Yes, that is true.

### 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.

### Why when you multiply an odd number by a even does it always equal a even?

When you multiply an odd number by an even number, you are essentially adding an even number of odd numbers together. Since adding an even number of odd numbers will always result in an even number, the product will be even.

### Is even number times even number always even?

Yes, it is. Any whole number times an even number will be even. This is because whole numbers can be represented as the product of their prime factors. Every even number contains 2 as a prime factor (thereby excluding all even numbers above 2 from being prime.) Additionally, the product of any two numbers is equal to the product of their prime factors. This means that the result of multiplying an even number by a whole number will always have a prime factor of 2, making it an even number.

### Will the product of 3 consecutive numbers always be even?

Yes because at least one of the consecutive numbers will be even, and if you times anything by an even number, the answer will always be even

### What do you know about the product of odd and even numbers?

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.