We are independent & ad-supported. We may earn a commission for purchases made through our links.
All The Science
Advertiser Disclosure
Our website is an independent, advertising-supported platform. We provide our content free of charge to our readers, and to keep it that way, we rely on revenue generated through advertisements and affiliate partnerships. This means that when you click on certain links on our site and make a purchase, we may earn a commission. Learn more.
How We Make Money
We sustain our operations through affiliate commissions and advertising. If you click on an affiliate link and make a purchase, we may receive a commission from the merchant at no additional cost to you. We also display advertisements on our website, which help generate revenue to support our work and keep our content free for readers. Our editorial team operates independently of our advertising and affiliate partnerships to ensure that our content remains unbiased and focused on providing you with the best information and recommendations based on thorough research and honest evaluations. To remain transparent, we’ve provided a list of our current affiliate partners here.
Science

What are the Divisibility Rules?

Tricia Christensen
By
Updated May 21, 2024
Our promise to you
All The Science is dedicated to creating trustworthy, high-quality content that always prioritizes transparency, integrity, and inclusivity above all else. Our ensure that our content creation and review process includes rigorous fact-checking, evidence-based, and continual updates to ensure accuracy and reliability.

Our Promise to you

Founded in 2002, our company has been a trusted resource for readers seeking informative and engaging content. Our dedication to quality remains unwavering—and will never change. We follow a strict editorial policy, ensuring that our content is authored by highly qualified professionals and edited by subject matter experts. This guarantees that everything we publish is objective, accurate, and trustworthy.

Over the years, we've refined our approach to cover a wide range of topics, providing readers with reliable and practical advice to enhance their knowledge and skills. That's why millions of readers turn to us each year. Join us in celebrating the joy of learning, guided by standards you can trust.

Editorial Standards

At All The Science, we are committed to creating content that you can trust. Our editorial process is designed to ensure that every piece of content we publish is accurate, reliable, and informative.

Our team of experienced writers and editors follows a strict set of guidelines to ensure the highest quality content. We conduct thorough research, fact-check all information, and rely on credible sources to back up our claims. Our content is reviewed by subject-matter experts to ensure accuracy and clarity.

We believe in transparency and maintain editorial independence from our advertisers. Our team does not receive direct compensation from advertisers, allowing us to create unbiased content that prioritizes your interests.

Divisibility rules can be simple and easy to remember tests you can perform on a number to determine if it will be evenly divided by another number. Some of these rules are quick to memorize and you probably already know some of them. For example, if the last digit of a number is even, you’re likely to be aware that the number can be evenly divided by 2. Another of the divisibility rules most people may know without thinking is that numbers ending in a 0 will always be divisible by 10 and by 5.

You can apply the following divisibility rules to numbers to help you determine whether you’ll get an even result:

A number will be divisible by 3 if the sum of the digits is divisible by 3.
Example: 228 is evenly divisible by 3 because 2 + 2 + 8 = 12 and 12 is divisible by 3.

4 will evenly divide a number if the last two digits of that number are divisible by 4.
Example: 788 is divisible by 4 because 88 is divisible by 4.

Any number ending in 0 or 5 will be evenly divided by 5, and 10 will evenly divide any number ending in 0.

If a number is divisible by 2 and 3, it is also divisible by 6.
Example: 180/2 = 90 and 180/3 = 60. Therefore 6 will also divide 180 evenly with a result of 30.

When the sum of a number’s digits equals a number divisible by 9, that number will always be divisible by nine.
Example: The number 621 has a digit sum of 9. 9 will divide 621 evenly with a result of 69.
You can take this divisibility rules for 9 to determine if 18 will evenly divide numbers. If both 2 and 9 will divide a number, 18 will also divide it.

The above examples are probably the easiest of the divisibility rules to remember. Others get significantly more complicated and may involved multiple manipulations of a number prior to deciding whether it can be evenly divided by a divisor. Sometimes it takes less time to simply do division than it does to apply one of the divisibility rules to a number, and these rules exist for very large numbers too. With complicated operations you can determine things like whether 71 or 79 will evenly divide other numbers.

The divisibility rules for 8 and 7 fall into this more complicated arena. For some math applications they may be useful. However, with smaller numbers you may simply want to do the division to determine if 8 or 7 are factors of these numbers.

All The Science is dedicated to providing accurate and trustworthy information. We carefully select reputable sources and employ a rigorous fact-checking process to maintain the highest standards. To learn more about our commitment to accuracy, read our editorial process.
Tricia Christensen
By Tricia Christensen
With a Literature degree from Sonoma State University and years of experience as a All The Science contributor, Tricia Christensen is based in Northern California and brings a wealth of knowledge and passion to her writing. Her wide-ranging interests include reading, writing, medicine, art, film, history, politics, ethics, and religion, all of which she incorporates into her informative articles. Tricia is currently working on her first novel.
See our Editorial Process Share Feedback

Related Articles

Discussion Comments
Tricia Christensen
Tricia Christensen
With a Literature degree from Sonoma State University and years of experience as a All The Science contributor, Tricia...
Learn more
All The Science, in your inbox

Our latest articles, guides, and more, delivered daily.

All The Science, in your inbox

Our latest articles, guides, and more, delivered daily.