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Mastering Divisibility: Simple Tricks for Quick Math Success

By Steven Darby - February 12, 2025

Math can sometimes feel like a puzzle, but knowing a few basic divisibility tricks can help you solve it faster and with greater confidence. Divisibility rules allow you to quickly determine if one number is divisible by another without performing full division. These tricks are especially helpful for simplifying fractions, factoring numbers, and solving problems more efficiently.

In this blog, we’ll explore some easy-to-follow divisibility rules that will make your math work a lot smoother!

1. Divisibility by 2

To determine if a number is divisible by 2, check if the last digit is even. Even numbers end in 0, 2, 4, 6, or 8.

Example:

456 → Last digit is 6 (even), so it is divisible by 2.
823 → Last digit is 3 (odd), so it is not divisible by 2.

2. Divisibility by 3

A number is divisible by 3 if the sum of its digits is divisible by 3.

Example:

123 → 1 + 2 + 3 = 6 (divisible by 3), so 123 is divisible by 3.
457 → 4 + 5 + 7 = 16 (not divisible by 3), so 457 is not divisible by 3.

3. Divisibility by 4

If the last two digits of a number are divisible by 4, then the whole number is divisible by 4.

Example:

124 → Last two digits are 24, and 24 is divisible by 4. Therefore, 124 is divisible by 4.
356 → Last two digits are 56, and 56 is divisible by 4, so 356 is divisible by 4.

4. Divisibility by 5

If a number ends in either 0 or 5, it’s divisible by 5.

Example:

85 → Last digit is 5, so 85 is divisible by 5.
142 → Last digit is 2, so 142 is not divisible by 5.

5. Divisibility by 6

A number is divisible by 6 if it’s divisible by both 2 and 3.

Example:

72 → It’s even (divisible by 2) and the sum of its digits (7 + 2 = 9) is divisible by 3. Therefore, 72 is divisible by 6.
100 → It’s even (divisible by 2), but 1 + 0 + 0 = 1, which is not divisible by 3. Therefore, 100 is not divisible by 6.

6. Divisibility by 9

A number is divisible by 9 if the sum of its digits is divisible by 9.

Example:

936 → 9 + 3 + 6 = 18 (divisible by 9), so 936 is divisible by 9.
721 → 7 + 2 + 1 = 10 (not divisible by 9), so 721 is not divisible by 9.

7. Divisibility by 10

A number is divisible by 10 if it ends in a 0.

Example:

110 → Ends in 0, so it is divisible by 10.
257 → Does not end in 0, so it is not divisible by 10.

8. Divisibility by 11

To check divisibility by 11, alternate subtracting and adding the digits of the number from left to right. If the result is divisible by 11 (or zero), then the number is divisible by 11.

Example:

2728 → 2 - 7 + 2 - 8 = -11 (divisible by 11), so 2728 is divisible by 11.
12345 → 1 - 2 + 3 - 4 + 5 = 3 (not divisible by 11), so 12345 is not divisible by 11.

Why Knowing Divisibility Rules Matters

Divisibility rules help you work smarter, not harder. By recognizing patterns in numbers, you can simplify complex problems, especially when factoring or reducing fractions. These tricks are also invaluable for doing mental math quickly and without the need for a calculator.

At Peak Learning Solutions, we believe that mastering math concepts can be an empowering journey, and small steps like learning divisibility rules can make a big difference in your confidence and skills. Keep practicing, stay curious, and remember that every challenge is an opportunity to grow.

If you ever need personalized guidance or academic coaching, we’re here to help you unlock your full potential. Call us at 720-737-9221 or visit www.peaklearningsolutions.com to learn how we can support your student’s academic success. Conveniently located at 6143 S Willow Dr, Greenwood Village, Colorado, we proudly serve students from Mountain Vista High School, Highlands Ranch High School, DSST Public Schools, and beyond.

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