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Make sure they do not show you the calculator's display. Stand across the room from the person and make it seem like you are trying to read their mind. For example, they could enter "123123." Dramatically announce this from across the room. Have them verify it and then tell the audience that you are right. For instance, if they entered 123123, then they would divide it by 11 and get 11,193. Announce from across the room that the result is divisible by 13. Tell them to do it on the calculator to prove it. For example, if their last result was 11,193, then they would divide it by 13 and get 861. Remember that they chose a 3-digit number and entered it twice. Make sure they only divide the result by 3-digits, rather than the 6 they entered at the beginning. For instance, if their last result was 861, and the original number was 123, they would divide 861 by 123 to get the number 7. Tell them without looking at the screen. Have them show the audience, if you have one, to prove that you are right. You can switch this trick up by having them divide the result by 7 in step 3, and announce that the result is 13 in the final step.

Summary:
Tell someone to secretly select a 3-digit number and enter it twice into a calculator. Announce that the number is divisible by 11 and have them check it. Tell them to divide that result by 13. Tell them to divide the result by the original 3-digit number. Announce that the final answer is 7.