Every prime number has a divisibility test. Many of these divisibility tests are slight variations of the following divisibility test for 7.
A divisibility test for 7 To determine whether a given base ten number is divisible by 7, double the ones digit of the given number. Find the difference between this number and the number formed by omitting the ones digit from the given number. If necessary, repeat this procedure until you obtain a small final difference.
If the final difference is divisible by 7, then the given number is also divisible by 7.
If the final difference is not divisible by 7, then the given number is not divisible by 7.
Example Use the above divisibility test to determine whether 301 is divisible by 7.
Solution The double of the ones digit is 2. Subtracting 2 from 30, which is the number formed by omitting the ones digit from the original number, yields 28. Because 28 is divisible by 7, the original number 301 is divisible by 7.
Use the divisibility test for 7, given above, to determine whether each number is divisible by 7.
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