The Divisibility tests exercise appears under the Pre-algebra Math Mission and Mathematics I Math Mission. This exercise practices fluency with the basic divisibility rules.
Types of Problems[]
There is one type of problem in this exercise:
- 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.
Strategies[]
Knowledge of the divisibility rules is intended for this problem, but it can be done with a calculator.
- A number is divisible by one, two, five, or ten if it's last digit is divisible by that same number.
- A number is divisible by three or nine if the sum of it's digits is divisible by three or nine respectively.
- A number is divisible by four if it's last two digits as a two-digit number are divisible by four.
- A number is divisible by six if it is divisible by both two and three.
- The proofs of these facts (except for six) can be performed by writing the expanded form of the number and performing some modular arithmetic.
- A number is also divisible by eight if its last three digits are.
Real-life Applications[]
- Divisibility knowledge leads to efficient work with fractions which have many applications in the real-world.
- Divisibility leads to man number theoretic concepts (such as primality) which can be used for encryption and other computer science applications.