whats prime?

53 is prime. The others factorize as follows:

57 = 3*19
87 = 3*29
91 = 7*13

Prime numbers are numbers that are divisible by themselves and 1.

The only prime number in that list is 53 as it can only be divided by itself (53) and 1.

57 is divisible by 1, 3, 19, 57
87 by 1, 3, 29, 87
91 by 1, 7, 21, 91

Prime number is a number that has 2 factors only.

53 = 1 x 53

57 = 1 x 57
57 = 3 x 19

87 = 1 x 87
87 = 3 x 29

91 = 1 x 91
91 = 7 x 13

∴ the answer is a)

The popular description is: a "prime" is a number that cannot be divided by anything else than itself or a unit.

The more precise description is: a prime is any number that cannot be described by two factors, unless one of the factors is a unit.

In counting numbers, the popular description works just as well as the more precise one. The only unit in counting numbers is 1.

87 = 3*29
87 can be written as two factors, none of them being 1; therefore 87 is NOT a prime.

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In integers, the more precise description is needed. Otherwise you could write 7 as
7 = (-7)*(-1) which are neither itself nor 1.

In integers, -1 is a unit. (You'll see that later)

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