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2 cannot be a factor of an odd number, 2 must be a factor of an even number.

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Q: How are odd and even products related to their factors?
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How are odd and even products related?

An even number can be divided by 2 evenly. An odd number will have a remainder of 1 when divided by 2.


What type of number has odd numbers as factors?

Both odd and even numbers may have odd numbers as factors.


Is the gcf of an odd and even number always even?

No. The opposite is true: the gcf of an odd number and an even number is always odd. All the factors of an odd number are odd; or to put it another way: If a number has an even factor, the number itself must be even. Thus the only common factors between odd and even numbers must be odd.


Are the factors of an odd number always odd?

Yes. An even number is defined as being evenly divisible by 2 (no fractional answers, only integers). If an odd number has an even factor, then because of the above definition, this odd number must have a factor of 2. But you will be hard pressed to find an odd number that is a multiple of 2, because that is already the definition of an even number. So, odd numbers cannot have even factors and thus odd numbers always have odd factors.


Why even divided by odd equal even?

Odd numbers do NOT have a factor of 2. When an Even number is divided by an Odd number with no remainder, the prime factors of the divisor cancel out the prime factors of the dividend, but there will be no prime 2 to cancel the prime factor of 2 in the dividend leaving the the quotient to have a factor of 2, and so will be Even. --------------------------------------------------------- Alternatively, consider what happens when you multiply Odd and Even numbers: Odd × Odd = Odd Odd × Even = Even Even × Even = Even The result is Even ONLY if at least one of the numbers multiplied together is Even. Thus if you divide an Even number by an Odd number, the result must be Even. Also consider that Odd times Odd is Odd. Multiplication is the inverse of division, so if you have: dividend ÷ divisor = quotient then dividend = quotient × divisor Now, if the divisor is Odd and the quotient is Odd, the the Dividend MUST be Odd (since Odd × Odd = Odd). Thus if the Dividend is Even and the Divisor is Odd, then the Quotient must be Even.

Related questions

How are odd and even numbers are related to their factors?

Even numbers must have 2 amongst their factors; they may have other even numbers amongst their factors. Odd numbers must not; every factor of an odd number must be odd.


How are odd and even products related?

An even number can be divided by 2 evenly. An odd number will have a remainder of 1 when divided by 2.


What is the meaning of even and odd factors?

All nonzero numbers have factors. Some factors are even numbers, some factors are odd numbers.


Is all factors of 48 even or odd?

48 has both even and odd factors.


Does even or odd numbers have more factors?

Some even numbers have more factors than some odd numbers and some odd numbers have more factors than some even numbers. As a group, even numbers have more factors than odd numbers.


Do odd or even numbers have more factors?

Some even numbers have more factors than some odd numbers and some odd numbers have more factors than some even numbers. As a group, even numbers have more factors than odd numbers.


Do odd numbers have a odd or even number of factors?

The number of factors can be either even or odd.


What type of number has odd numbers as factors?

Both odd and even numbers may have odd numbers as factors.


What you know about the factors when the products are square numbers?

There will be an odd number of different factors.


Is the greatest common factor of any 2 odd numbers odd?

Not only can they, but they must. An odd number cannot have an even factor. So none of the factors of either of the two odd numbers can be even and so the GCF is made up of only odd factors and so it must be odd.


What does 31 have odd or even number of factors pairs?

Odd.


Do odd numbers have an odd or even number of factors?

Both. 9 has three factors. 11 has two factors.