Find the remainder of $9^2\cdot 13\cdot 21^2$ when divided by $4$ 
Find the remainder of $9^2\cdot 13\cdot 21^2$ when divided by $4$

How should I approach this type of questions?
Without calculator of course
I did this:
$9^2\cdot 13\cdot 21^2=81\cdot 13\cdot 441=81\cdot 5733=464,373=33\bmod 4=1 \bmod 4$

Hint: What is $9\bmod 4$? What is $13\bmod 4$? 
How would you proceed from here?

Also, you wrote that $464\,373=1\bmod 4$. Always keep in mind that the "$=$" sign means that two things are exactly the same, in every way. In stead one should write 


*

*$\overline{464\,373}=1\bmod 4$, 

*$464\,373\bmod 4=1\bmod 4$,

*$\overline{464\,373}=\overline 1$ (when it is understood that we are working in $\mathbb Z/4\mathbb Z$)


or


*

*$464\,373\equiv 1\bmod 4$.

