Divisibility Rules Explained

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Divisibility Rule for 3, 9, 7 and 11 - Why they work?

Divisibility by 3 and by 9: Why do they work?
Most everyone seems to know the rule for divisibility by three: add up the digits and see if the sum is a multiple of three.
Most seem to “know” that the same rule holds for nine.
But why do these rules work? And did you know that summing the digits tells you a bit more than just a yes/no answer?

Divisibility Rule for Seven
Many folk know divisibility rules for 3, for 5, for 9, for 11 and so on, but what about a divisibility rule for the number 7. There is one, and here it is! (Plus, you’ll learn from this how to create your own divisibility rules for 13, and 17, and 43, and 97 and the like!)

Divisibility by 11
In this video I explain the standard divisibility rule for the number eleven. (Did you know that every palindrome with an even number of digits must be a multiple of eleven?)

Dividing by Nine: Something Cute
Here is something not too serious, but cute. To divide a number by 9, just add up its digits in turn! For example:
124 / 9 = “1 and 1+2 and 1+2+4” = 13R7
Let’s explore why this little curiosity work

Dividing by 97 - and other such Numbers
Students need help “standing back” and seeking perspective on matters. It is easy to get locked into memorisation and procedure. This little video is just a tidbit that helps in this regard. It provides an easy example of the power that can result in pausing to think about things first before diving in. Dividing big numbers by 97 is actually fairly straightforward. This is not a technique to be memorised, but a statement about thinking!

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