Final review: divisibility of numbers
Divisibility tests: by 2 — the last digit is even; by 5 — the last digit is 0 or 5; by 10 — the last digit is 0; by 3 and 9 — the digit sum is divisible by 3 or 9 respectively. A prime number is divisible only by 1 and itself. Factoring a composite number into primes helps to find the GCD and LCM: the GCD takes the common prime factors with the smallest powers, the LCM takes all prime factors with the greatest powers. Always a · b = GCD(a, b) · LCM(a, b). If a number is divisible by both 2 and 3, it is divisible by 6, because 2 and 3 are coprime.
“Digit detective”: each group gets a four-digit number and finds, without dividing, which of 2, 3, 5, 9, 10 divide it. Another group checks by dividing. The group with the most correct answers wins.