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**SlipEternal** A possibly simpler rule for divisibility by 7 is this: Take the last two digits mod 7. Subtract three times that from the leftmost digits (without the right-most two). If that is divisible by 7, then the whole number is divisible by 7.

Example: 4,571. 71 = 70+1. 45-3*1 = 42 is divisible by 7, so 4,571 is, as well. $4,571 = 7\cdot 653$.

Example: 4,249. 49 = 49+0. 42-3*0 = 42 is divisible by 7, so 4,249 is, as well. $4,249 = 7\cdot 607$.

Example: 4,781. 81 = 77+4. 47-3*4 = 35 is divisible by 7, so 4,781 is, as well. $4,781 = 7\cdot 683$.