Starting from the end of the number, multiply the last digit by 2 and add the product to the next digit. Multiply the sum found by 2 and add to the next digit until the first digit. If the end result is divisible by 19 then the whole number is divisible by 19. For example, take 373977. 7*2=14+7=21*2=42+9=51*2=102+3=105*2=210+7=217*2=434+3=437. 7*2=14+3=17*2=34+4=38 divisible by 19, so 373977 is divisible by 19.
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