an odd number is a number where the last digit ends in 1, 3, 5, 7, or 9
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There is no such pattern because there are no even odd numbers. Odd numbers, by definition, are odd and therefore, not even.
All even numbers have 2 as a factor - that is in their definition No odd numbers have 2 as a factor - that is in theirs. Trying to divide 2, or any multiple of it, into a number that by definition cannot be divided by 2, is a hopeless endeavour. There is no guarantee that you can divide an even number by an odd one, but it is not impossible.
No. For example, 5+5=10.
Square numbers have odd numbers of factors. Examples: 4, 9, 16
An even number can be divided by 2 evenly. An odd number will have a remainder of 1 when divided by 2.