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Every integer is a rational number.
Every integer is rational.
Yes, 1 is a factor of every integer and every integer is a multiple of 1.
No, not every negative number is an integer. For example, -11/2 is not an integer. However, -1, -2, -3, and so on, are negative integers. Perhaps that is what you meant to ask. The negative of every positive integer is a negative integer.
Every counting number IS an integer.