Thursday, 16 March 2017

Born to do Math 9 - 1,001 and the Box (Part 7)

In-Sight Publishing
Born to do Math 9 - 1,001 and the Box (Part 7)
Scott Douglas Jacobsen & Rick Rosner
March 16, 2017

[Beginning of recorded material]

Rick Rosner: Here’s how to quickly dissect a number, division-wise. In elementary school, you probably learned that if the digits of a number of add up to 3, then it’s divisible by 3. You may not remember that. But that’s the deal. If the digits of a number add up to 9, then it’s divisible by 9. There are some bunch—of, of, of, not a bunch but—several other tricks. If you look at the last digit of a number, you can tell if it is divisible by 2, 5, or 10.

If you look at the last 2 digits of a number, you can tell whether it is divisible by 2 or 4, or 5 or 25, or, obviously, 100. The last three digits of a number whether it’s divisible by 2, 4, or 8, or 5, 25, or 125, or 10, 100 and a 1,000. By combining things, you can get divisibility by 6, divisibility by 12. It’s all of those little tricks, which are pretty much—if you were betting people in a bar just by applying those little tricks to a number and the number is resistant to division by all of the numbers that we went into, then it is probably prime.

There’s on more trick, which is fun if you’re a math geek like me. Which is if the odd digits of a number add up to be the same as the even digits of a number, that number is divisible by 11. By that, I mean, take 154, the first digit is 1. The second digit is 2. The third digit is 3. 1 plus 4 equals 5, which equals the second digit. 154 is divisible by 11. 1,331 is divisible by 11 because the 1 and the 3 add up to the same as the 3 and the 1.

Which also means that any number that’s a palindrome with an even number of digits is divisible by 11, and oh! If the digits in a number differ by a multiple of 11, if some of the odd digits differ from some of the even digits by a multiple of 11—0, 11, 22, 33—that number is also divisible by 11. So 4,224, divisible 11. 135,531, divisible by 11 because the 1, the 3, and 5 add up to the 3, and the 5, and the 1. If your friends are easily impressed, then do something with that. 

[End of recorded material]
Rick Rosner
American Television Writer
Rick Rosner
Scott Douglas Jacobsen
Editor-in-Chief, In-Sight Publishing
In-Sight Publishing
[1] Four format points for the session article:
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  2. Session article conducted, transcribed, edited, formatted, and published by Scott.
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  4. This session article has been edited for clarity and readability.
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