Question

Why prime factors are always less than square root of number?

Answer 1

But you can show that when thenumber is not prime, the smallestprime divisor less than the numberitself is less than or equal to thesquare root. Let be a positive composite integer and be the smallestprime factor of less than itself. ... Then either is prime or a product of primes

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Answer 2

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because it leaves a remainder of 1 when divided by any of them. But the previous lemma says that every number greater than 1 is divisible by a prime. Every composite number has a proper factor less than or equal to its square root.