Question 1207735: Greg finds the value of 708*709*710*711 and then divides the result over 712. What is the remainder? Is it possible to do this using mental math only?
Answer by math_tutor2020(3816)   (Show Source):
You can put this solution on YOUR website!
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) = 24 (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: 24
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