Divisibility
Divisibility rules are shortcuts that determine whether a whole number divides evenly by 2, 3, 5, 9, or 10 without performing long division. In Grade 6 Saxon Math Course 1 (Chapter 3: Number, Operations, and Geometry), students learn last-digit rules: a number ending in 0, 2, 4, 6, or 8 is divisible by 2; ending in 0 or 5 means divisible by 5; ending in 0 means divisible by 10. For divisibility by 3 or 9, add all digits—if the sum is divisible by 3, the number is; if the digit sum is divisible by 9, the number is too. These rules speed up fraction simplification and factor identification.
Key Concepts
New Concept A number is divisible by another if it can be divided without a remainder. These rules are shortcuts to find factors without division.
Last Digit Tests A number is divisible by: $2$ if the last digit is even. $5$ if the last digit is $0$ or $5$. $10$ if the last digit is $0$.
Sum of Digits Tests A number is divisible by: $3$ if the sum of the digits is divisible by $3$. $9$ if the sum of the digits is divisible by $9$. What’s next Next, you will apply these rules in worked examples and practice problems to quickly test any number for its factors.
Common Questions
What is the divisibility rule for 2?
A number is divisible by 2 if its last digit is even: 0, 2, 4, 6, or 8. Example: 348 ends in 8, so it is divisible by 2.
How do you check if a number is divisible by 3?
Add all the digits. If the sum is divisible by 3, the original number is too. For 123: 1+2+3=6, and 6 is divisible by 3, so 123 is divisible by 3.
What is the divisibility rule for 9?
Add all digits. If the sum is divisible by 9, the number is too. For 729: 7+2+9=18, and 18÷9=2, so 729 is divisible by 9.
How does divisibility by 5 work?
A number is divisible by 5 if its last digit is 0 or 5. Examples: 35 (ends in 5) and 80 (ends in 0) are both divisible by 5.
Is 462 divisible by both 2 and 3?
Yes. It ends in 2 (divisible by 2). Its digit sum is 4+6+2=12, which is divisible by 3, so it is also divisible by 3.
Why are divisibility rules useful in Grade 6 math?
They help students quickly find factors, simplify fractions, and verify answers without performing full long division.