3 ms·
Another quick way to check divisibility by 7 is to multiply each digit by 3^x where x is the place (right to left). Good way to check divisibility in your head
by joeax 11y ago
Another quick way to check divisibility by 7 is to multiply each digit by 3^x where x is the place (right to left). Good way to check divisibility in your head and useful up to 4-5 digits.
As an example, consider 413:
4x9 + 1x3 + 3 = 36 + 3 + 3 = 42
42 is divisible by 7 therefore 413 is too.
- Jtsummers 11y ago10 = 3 (mod 7) So this works because you're substituting the powers of 10 with powers of 3, and we're operating under mod 7 arithmetic. Conveniently, this can also be repeated like drfuchs' method if your numbers are too large to recognize as a multiple of 7 after the first pass. 413 => 4*9+1*3+3 = 42 => 4*3+2 = 14 => 1*3+4=7
- hardlianotion 11y agoWe used to call this casting out nines.