Question

Write whether every even number except 2 is prime or compound.​

Answer 1

Answer:

Yes, any even positive integer except for 2 is a composite number. Composite numbers are positive integers greater than 1 that are exactly divisible, i.e., a zero remainder, by other positive integers besides just itself and 1, for example, the next even positive integer after 2 is 4; Four (4) is a composite number because it is a positive integer that is exactly divisible by not only itself and 1, but also by 2: 4/4 = 1, 4/1 = 4, 4/2 = 2. Six (6), the next even positive integer, is a composite number because it is a positive integer that is exactly divisible by not only itself and 1, but also by 2 and 3: 6/6 = 1, 6/1 = 6, 6/3 = 2, and 6/2 = 3. In general, every even positive integer greater than 2, 2n, is a composite number, where n is a positive integer ≥ 2, because it is exactly divisible, i.e., a zero remainder, by other positive integers besides just itself and 1; It is exactly divisible by at least itself, 1, and 2: 2n/2n = 1, 2n/1 = 2n, and 2n/2 = (2/2)n = (1)n = n.

NOTE: Since composite numbers by definition must be positive integers, then zero (0) and all even negative integers, e.g., -2 and -4, could NOT be considered in this discussion.

Answer 2

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• Every even number except 2 is Composite number.

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