When $(5k+1)^2$ is divided by $5$,the remainder is . . . . . . .

For any two positive integers $a$ and $b$,what is the relationship between their $HCF$ and $LCM$? $\text{HCF}(a, b) \times \text{LCM}(a, b) = \text{?}$

Every composite number greater than $1$ can be expressed (factorized) as a product of primes,and this factorization is .........,apart from the order in which the prime factors occur.

The value of $\sqrt{1+1}$ is.......

If the Least Common Multiple $(LCM)$ of $(12, 15, 21) = 500 + 2x$,then $x = $ . . . . . .

Find the $HCF$ and $LCM$ of the integers $336$ and $54$ and verify that $HCF \times LCM = \text{product of the two integers}$.