Divisibility tests

The  exercise appears under the Pre-algebra Math Mission. This exercise practices fluency with the basic divisibility rules.

Types of Problems
There is one type of problem in this exercise:


 * 1) Determine if number is divisible by another number: This problem has a large integer and asks if it is divisible by some smaller integer. The student determines whether it is or not and answers yes or no.Divtes1.png

Strategies
Knowledge of the divisibility rules is intended for this problem, but it can be done with a calculator.
 * 1) A number is divisible by one, two, five, or ten if it's last digit is divisible by that same number.
 * 2) A number is divisible by three or nine if the sum of it's digits is divisible by three or nine respectively.
 * 3) A number is divisible by four if it's last two digits as a two-digit number are divisible by four.
 * 4) A number is divisible by six if it is divisible by both two and three.
 * 5) The proofs of these facts (except for six) can be performed by writing the expanded form of the number and performing some modular arithmetic.

Real-life Applications

 * 1) Divisibility knowledge leads to efficient work with fractions which have many applications in the real-world.
 * 2) Divisibility leads to man number theoretic concepts (such as primality) which can be used for encryption and other computer science applications.