A divisibility test for 13 To determine whether a given base ten number is divisible by 13, multiply the ones digit of the given number by 4. Find the sum of this multiple of 4 and the number formed by omitting the ones digit from the given number. If necessary, repeat this procedure until you obtain a small final sum.
If the final sum is divisible by 13, then the given number is divisible by 13.
If the final sum is not divisible by 13, then the given number is not divisible by 13.
Example Use the divisibility test for 13 to determine whether 1079 is divisible by 13.
Solution Four times the ones digit is 36. The number formed by omitting the ones digit is 107. The sum of 36 and 107 is 143. Now repeat the procedure on 143. Four times the ones digit is 12. The sum of 12 and 14, which is the number formed by omitting the ones digit, is 26. Because 26 is divisible by 13, the original number 1079 is divisible by 13.
Use the divisibility test for 13 to determine whether each number is divisible by 13.
1885
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