Number of ordered pairs $(a,b)$ such that $ab \le 3600$ Find number of ordered pairs $(a,b)$ such that $ab\le 3600$ and $a,b \in N$
My attempt : Well, all $a,b \leqslant 60$ are solutions. These 3600 solutions. After that I have no idea how to count the number of remaining solutions... 
I have a feeling that my approach is $very$ bad. But I had to give as it would be marked as off-topic.

Hint:  First, you can count only those pairs where $a \lt b$, double them, and add one for $(60,60)$  We know $a \lt 60$.  How many are there for $a=1$?  How many are there for $a=2$?  Can you write an expression for general $a$?  Then add them up for $a$ from $1$ to $59$.
