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Why is the product of an even number and any other number always even?
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.
Why does an even times an even always equal an even answer?
Having a factor of 2 defines an even number. Multiplying anything that has a factor of 2 by anything else will create a product that has a factor of 2, which will be by definition an even number.
Is the greatest common factor of two even numbers always even?
Assuming the second even number is equal to 4 or greater, than the highest common factor of the two numbers is equal to an even number 2 or greater. Why can't an odd factor be used? Any odd factor must be multiplied by (at least) 2 to create an even product (ie. the 1st even number). That same odd factor must be multiplied by (at least 2) and any other number to create a 2nd even product, thereby making the Greatest Common Factor (at least) 2 times the odd number....which is an even number.
Is the product of two odd numbers odd or even?
The product of two odd numbers is always odd.
Is the greatest common factor of any even numbers always even?
Yes.
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.
Why is the product of an even number and any other number always even?
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.
Why does an even times an even always equal an even answer?
Having a factor of 2 defines an even number. Multiplying anything that has a factor of 2 by anything else will create a product that has a factor of 2, which will be by definition an even number.
Is the greatest common factor of two even numbers always even?
Assuming the second even number is equal to 4 or greater, than the highest common factor of the two numbers is equal to an even number 2 or greater. Why can't an odd factor be used? Any odd factor must be multiplied by (at least) 2 to create an even product (ie. the 1st even number). That same odd factor must be multiplied by (at least 2) and any other number to create a 2nd even product, thereby making the Greatest Common Factor (at least) 2 times the odd number....which is an even number.
When you multiply any number of even numbers will the product always be odd?
No, the product will always be even.
Can an odd product ever have an even factor?
No.
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.
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.
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.
Will the greatest common factor of an odd and even number always be even?
No, always odd.
Is the greatest common factor of two even numbers always sometimes or never even?
Always even.
Is the greatest common factor of an odd and even number always 1?
No, the GCF of an odd an even number is not always 1. Odd and even numbers can share factors other than 1. For example, the greatest common factor of 5 and 10 is 5.
