Question

The smallest positive divisor greater than 1 of a composite number 'a' is ______

• A. $<\sqrt{a}$
• B. $=\sqrt{a}$
• C. $>\sqrt{a}$
• D. $\le \sqrt{a}$

Answer 1

Answer: (D)

$\le \sqrt{a}$

For square of a prime number the smallest divisor is $\sqrt{a}$ as it has only three divisors $1,\sqrt{a},a$ so it is $\sqrt{a}$

For a square of composite number as $\sqrt{a}$ is composite it has fctors less than $\sqrt{a}$ which is also a factor of $a$ so it is $<\sqrt{a}$

For a composite not a perfect square

Let $a=p\times q$

$p,q$ are integers not equal to $1$ with $p<q$

Then $p<\sqrt{a},q>\sqrt{a}$ as $p.q=a$

So it is $<\sqrt{a}$

Hence answer is $\le \sqrt{a}$