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algorithm,yet they are fun,and,belie ve it or not,can come in handy. You must present this unit as a “fun unit” so that students will not see this as something that they must memorize. Rather,the y should try to understand the underpinnings of the rules.

Let us consider the rule for divisibility by 7 and then,as we inspect it, see how this can be generalized for other prime numbers.

Rule for Divisibility by 7 Delete the last digit from the given number and then subtract twice this deleted digit from the remaining number. If the result is divisible by 7, the original number is divisible by 7. This process may be repeated if the result is too large for simple inspection of divisibility of 7.

Let’s try one as an example of how this rule works. Suppose we want to test the number 876,547 for divisibility by 7.

Begin with 876,547 and delete its units digit,7,and subtract its double, 14,from the remaining number: 87654 ? 14 = 87640. Since we cannot yet visually inspect the resulting number for divisibility by 7,we continue the process.

Continue with the resulting number 87640 and delete its units digit,0,and subtract its double,still 0,from the remaining number; we get 8764?0 = 8764. Since this did not change the resulting number,8, 764,as we seek to check for divisibility by 7,we continue the process.

Continue with the resulting number 8,764 and delete its units digit, 4,
and subtract its double,8,from the remaining number; we get 876 ? 8 = 868. Since we still cannot visually inspect the resulting number,868,for divisibility by 7,we continue the process.

Continue with the resulting number 868 and delete its units digit,8,and subtract its double,16,from the remaining number; we get 86?16 = 70, which is divisible by 7. Therefore,the number 876,547 is divisible by 7. Before continuing with our discussion of divisibility of prime numbers, you ought to have students practice this rule with a few randomly selected numbers and then check their results with a calculator.

Taken From :Math Wonders to inspire teacher and student