32-bit vs 64-bit processor/machine

[markthien]

Hi guys,

I know that 64-bit processor has more transistor than a 32-bit processor and by using 32 bits your processor can represent numbers from 0 to 4,294,967,295 while a 64-bit machine can represent numbers from 0 to 18,446,744,073,709,551,615. Obviously this means your computer can do math with larger numbers, and be more efficient with smaller numbers.

The question is how can it be more efficient with smaller numbers? Can anyone give an example on this in term of math or programming?

Thanks!

Cheers,
Mark