Prove that a positive integer n is prime, if no prime p less than or equal to root n divides n.

Let us proof the result using contradiction.

Let n ≥ 0 be a composite number.

∴ n has a factor a such that 1 < a < n.

i.e., we can write n = ab, where a and b are positive integers and 1 < a, b< n.

We may assume that b ≤ a.

Hence our supposition was wrong.

Thus, for every positive integer n  prime , if no prime p less than or equal to root n divides n