Express the number $7429$ as a product of its prime factors.

According to Euclid's division lemma,for given positive integers $a$ and $7$,there exist unique non-negative integers $q$ and $r$ such that $a = 7q + r$; where..........

Express the number $3825$ as a product of its prime factors.

If $a$ and $b$ are two odd positive integers such that $a > b,$ then prove that one of the two numbers $\frac{a+b}{2}$ and $\frac{a-b}{2}$ is odd and other is even.

Use Euclid's division lemma to show that the cube of any positive integer is of the form $9m, 9m+1$ or $9m+8$.

Check whether $6^n$ can end with the digit $0$ for any natural number $n$.