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