Most efficient way to solve finding the missing number without calculator?

[shivajikobardan]

This is the question.
The way the instructor solved this was using:
Separate each columns.
Then first row/third row x second row
Are there other pattern matching and arithmetic techniques to solve this in your opinion?
Note calculator cannot be used.

 

[Dr.Peterson]

A puzzle like this requires trying many possibilities, and even then you can't be sure the pattern you found is what was intended. There is no general method to teach. (And calculators make no difference.)

What I just did was to factor each number, since it looked like there could be a pattern of that sort, and I noticed that in the first and third columns, the product of the top two numbers equals the product of the bottom two numbers, and that the second column easily fits that pattern. I see no pattern in each row.