Yes -11 is an integer which means a whole number.
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11 is an integer.
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.
11 x 11 = 121. Any integer multiplied by itself results in a square number.
That means that if you divide the number by 11 (integer division), you get a zero remainder. To obtain such numbers, multiply any integer by 11: 0 x 11 = 0 1 x 11 = 11 2 x 11 = 22 3 x 11 = 33 etc.
11 is a prime number. For it to be relatively prime, it needs to be compared to another integer.