Determining If a Large Number is Divisible by 11Date: 10/22/2003 at 11:55:28 From: Concerned math student Subject: 57986*11=637846?????? I just learned a trick to decide whether a large number is divisible by 11 or not. Here's an example to decide if 637846 is divisible by 11: 637846 Cross out the last two digits (46) and add them to your remaining total: 6378 + 46 = 6424 Cross out the last two digits (24) and add them to your remaining total. 64 + 24 = 88 88 is divisible by 11, so the number 637846 is also divisible by 11. Why does this method work? Date: 10/22/2003 at 12:35:27 From: Doctor Peterson Subject: Re: 57986*11=637846?????? Hi, Concerned. This is related to the more familiar divisibility check listed in our FAQ: Divisibility Rules http://mathforum.org/dr.math/faq/faq.divisibility.html You can prove it by considering the rightmost two digits of a number (your 46) as a number y (less than 100), and the other digits (6378 in your example) as another number x. Then the number you are starting with is equal to: 100x + y When you take just the left part, and add to it the right part, you have: x + y Now think about the difference between these two numbers: (100x + y) - (x + y) = (100x - x) + (y - y) = 99x Since this difference is always a multiple of 11, then if one of the numbers is divisible by 11, so is the other. As a result, your original number 100x + y is divisible by 11 if and only if the new, smaller number, x + y, is divisible by 11. Repeat the process until you get a number small enough to tell by sight whether it is. If you have any further questions, feel free to write back. - Doctor Peterson, The Math Forum http://mathforum.org/dr.math/ |
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