Answer to Question #200363 in Discrete Mathematics for Adrienne Buatona

Question #200363

Determine if 1781 is divisible by 3, 6, 7, 8, and 9


1
Expert's answer
2021-06-01T01:39:42-0400

Let us determine if 1781 is divisible by 3, 6, 7, 8, and 9.


Since the last digit 1 is odd, we conclude that 1781 is not divisible by 2, and hence 1781 is not divisible by "6=2\\cdot 3" and 1781 is not divisible by "8=2\\cdot 4".


Since the sum "1+7+8+1=17" of digits is not divisible by 3 (and hence by 9), we conclude that 1781 is not divisible by "3" and 1781 is not divisible by "9".


Taking into account that "178-2\\cdot 1=176", "17-2\\cdot 6=5", and "5" is not divisible by 7, we conclude that 1781 is not divisible by 7.



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