Divisibility of sums, differences and products; tests for 4, 8, 6 and 11

In the Russian programme (Grade 6; more in Grade 7) the properties of divisibility are taught: if every term is divisible by a number, so are the sum and difference; if at least one factor is divisible, so is the product. The converse is false: a sum can be divisible although the terms are not (3 + 7 = 10 is divisible by 5).

Tests: by 4 if the last two digits form a number divisible by 4; by 8 if the last three digits do; by 6 if the number is even and its digit sum is divisible by 3; by 11 if the sum of the digits in odd places minus the sum in even places is divisible by 11. The tests for 2, 3, 5, 9 and 10 are from Grade 5.

Common slips: thinking one divisible term is enough for a sum; testing 6 by the last digit only; testing 4 by the last digit.