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.

Solution 1:

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 $59$.