PR-0563IRE Developing Algebraic Thinking

DIVISIBILITY RULES
Teachers notes
Introduction
Looking at
the algebra
We often need to know quickly whether one number will divide evenly
into another number. Knowing simple divisibility rules can make later
factoring tasks in algebra much easier. The activities in this section
provide opportunities to use the most common divisibility tests to create
numbers satisfying the rules. Starting with tasks involving a limited
number of tiles and divisibility rules, the pages become increasingly
more difficult until all 10 number tiles are used.
A number is said to be divisible by another number if and only if the
first number divides evenly into the second number, leaving a remainder
of 0. Divisibility tests are helpful in algebra when pupils begin factoring
various polynomials. Below is a list of the most common divisibility
rules.
A number is divisible by:
• 2, if it ends with an even number in the ones place. That is, the ones
digit is 0, 2, 4, 6, or 8.
Examples: 54, 806, 3798.
• 3, if the sum of the digits in the number is divisible by 3.
Examples: 57, 321, 5412.
• 4, if the last two-digit number is divisible by 4.
Examples: 124, 6380, 999912.
• 5, if the ones digit is 0 or 5.
Examples: 75, 200, 4070, 99995
• 6, if the number is divisible by 2 and by 3.
Examples: 48, 234, 7236.
Viewing Sample
• 8, if the last three-digit number is divisible by 8.
Examples: 1240, 3568, 765032.
• 9, if the sum of the digits in the number is divisible by 9.
Example: 468, 5247, 71559.
• 10, if the number ends in 0.
Example: 50, 700, 4080.
Tests for 7, 11, and other numbers do exist, but they are sometimes very
awkward to use. Long division or using a calculator are often quicker.
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