Another example. Is 3647 divisible by 7?
3647 -> 364 + (7 x 5) = 399 399 -> 39 + (9 x 5) = 84, which is a multiple of 7. Therefore 3647 is also a multiple of 7 (and incidentally, so is 399).I shall call this algorithm “Multiply by 5 and add”.The algorithm “Multiply by 2 and subtract” also works as a test for divisibility by 7:3647 -> 364 – (7 x 2) = 350 350 -> 35 – (0 x 2) = 35, which is a multiple of 7 Therefore 3647 is also a multiple of 7 (and incidentally, so is 350).These two algorithms form a “conjugate pair”, one being “add” and the other being “subtract”, as well as one being “multiply by m” and the other being “multiply by (p-m)”, where p in this case is 7.All this is leading up to the remaining divisibility tests. Each one uses the basic procedure of chopping off the units digit, multiplying it by m [or (p-m)] and then either adding to or subtracting from the truncated number.Why These Methods WorkThe simplest explanation, which is usually good enough for children, is that the procedure is just a fancy way of doing
