Question 1207735
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This is possible without a calculator. 
It can be done really quickly after you get enough practice.


708 is 4 short of 712, so we can say 708 = -4 (mod 712). 
The "mod" refers to "modular arithmetic". 
It is very useful when dealing with remainders. 
709 is 3 short of 712, so 709 = -3 (mod 712).
And so on.


Therefore 708*709*710*711= (-4)*(-3)*(-2)*(-1) = <font color=red>24</font>  (mod 712)


Whatever massive number 708*709*710*711 turns out to be, dividing it over 712 yields some quotient with remainder 24.
Throughout the modular arithmetic process, we ignore the quotient.


Answer: <font color=red>24</font>
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