Divisibility
Divisibility rules and tests
Start with the basics and progress through 5 lessons. Each lesson builds on the previous one.
0 of 5 lessons done
Test Your Knowledge
10 questions, new mix each time (from 85)
In This Topic (5 lessons)
Divisibility Rules
Learn quick tricks to tell if a number divides evenly into another without doing long division.
Divisibility by 2, 5, and 10
Learn the quick rules to tell if a number is divisible by 2, 5, or 10 just by looking at its last digit.
Divisibility by 3 and 9
Learn the digit sum rule: add the digits of a number to see at once whether it is divisible by 3 or by 9, find missing digits and check your sums.
Divisibility by 4, 6, and 8
Test any whole number for 4, 6 and 8 in seconds: read the last two or three digits, or combine the rules for 2 and 3, and see why it works.
Combined Divisibility Rules
Combine simple rules to test for 12, 15, 18 and 36, learn the alternating sum rule for 11, and find every divisor from 2 to 12 in seconds.
Divisibility rules are shortcuts to determine if one number divides evenly into another without doing long division. These rules for 2, 3, 4, 5, 6, 8, 9, and 10 speed up mental math and are foundational for understanding factors and multiples.
What You'll Learn
- Apply divisibility rules for 2, 3, 5, and 10
- Apply divisibility rules for 4, 6, 8, and 9
- Test divisibility without dividing
- Use divisibility to simplify fractions
- Solve problems using divisibility
Frequently Asked Questions
What is the rule for divisibility by 3?
A number is divisible by 3 if the SUM of its digits is divisible by 3.
What is the rule for divisibility by 4?
A number is divisible by 4 if its LAST TWO DIGITS form a number divisible by 4.
Why do divisibility rules work?
They exploit patterns in our base-10 number system.