A number is even if it ends in two, four, six, eight, or zero. A number is odd if it ends in one, three, five, seven or nine.
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Even. There are several ways to determine whether an integer is even or odd, all of which indicate that 0 is an even number: it is a multiple of 2, it is evenly divisible by 2, it is surrounded on both sides by odd integers, and it is the sum of an integer with itself. See related links for detailed proof.
It will always be odd. A proof: Call the even number m, call the odd number p. 'p' is equal to an even number 'n' + 1. Adding m and p is equal to m + n + 1; since m and n are both even, their sum is also even (see the related questions). m + n + 1 is one more than an even number, so it is odd, and therefore an odd number plus an even number is also always odd. QED
all even numbers can be written in the form 2k where, k is an integer. all odd numbers can be written in the form 2j+1, where j is an integer. 2k + 2j + 1 = 2(k+j) + 1. You can see that this is in the form of an odd number. hence, the sum of an odd number and an even number is always odd. Test the theory. Pick any even and any odd number. Add them. The total will always be odd.
Do you see that ' 7 ' on the end of 127 ? That ' 7 ' is odd, so the entire number is odd. It doesn't matter how many other numbers come before the ' 7 ' or what they are.
Alternate number sequence. Numbers ending in 0,2,4,6,8 are EVEN Numbers ending in 1,3,5,7,9 are ODD Hence 0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20 et seq..,, Are alternative Even and Odd. e.g. A number such as 1213 is Odd because it ends in ;3; A number such as 1,234,568 is Even because it ends in '8'.