10 easy division tricks for large and small numbers

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Once mastered, these division tricks will make basic math a breeze! Whether your student needs help with quick calculations or is memorizing their math facts, it comes in handy to have one or two “math hacks” ready to go!

Division skills are a staple of elementary math for good reason: the number sense and logical skills students build by learning to divide are key to advancing their math skills. Like virtually any STEM subject, math concepts build upon each other like rungs of a ladder. 

To get to the next level, it’s essential to learn the concepts that will help them understand what’s ahead! Division, just like multiplication and graphing quadratic equations, is a core skill in any budding mathematician’s tool kit. 

That said, division isn’t always easy! Especially when dealing with more and more complex numbers, learning to divide can be frustrating and require just as much eraser as pencil. 

So, let’s take some of the stress out of the process with some useful division tricks that are great to have in your back pocket for school and any situation that requires some low-tech math!

Useful dividing tricks 

We’ll walk through division shortcuts for numbers 1-10 that will be great to share with kids. Not only will these perhaps boost their confidence (and hopefully quiz scores), they’ll have speedy mental calculation ready for their next math competition

And there’s no denying that now is an excellent time for many students to get some extra math support and tutoring!

According to a recent McKinsey study, students are about five months behind in math due to the impacts of COVID-19. So, a little creativity and a few tips and tricks can’t hurt, right? 

Along with everyday ways to make math fun, encouraging kids to try a few math games and activities can go a long way towards catching up and even enjoying math class! 

With that in mind, here are a few division shortcuts that can help students learn how numbers work and get the hang of those mathematical building blocks. 

Dividing by 1 

An important one to remember (if you’ll excuse the pun): any number divided by 1 is the number itself! For instance, 300 divided by 1 is 300.

Dividing by 2

Every even number is divisible by 2; that’s any number ending in a 0,2,4,6, or 8. For instance, 566 can be evenly divided by 2: 283. 

Dividing by 3

Here’s a lesser known fun fact: if the sum (the total of numbers added together) in a given number can be divided by three, so can the number!

Here’s an example : The number is 21. 2+1 = 3. 21 divided by 3 = 7. 

Skeptical? Let’s look at a bigger number: 423. 4+2+3 = 9. 423 divided by 3 = 141. 

Dividing by 4

When dividing by 4, look at the last two digits of the number. Are those two digits divisible by 4? That means the entire number is as well!

For example, let’s look at a crazy long number like 5601120. 20 is divisible by 4, and so is 5601120! 5601120 divided by 4 is 1400280. 

Dividing by 5

Another great one to remember: any number that ends in a 0 or a 5 is always divisible by 5. Just like 10 is divisible by 5, so is 82984780 (the quotient is 16,596,956). 

Dividing by 6 

This division hack has two steps, but it’s worth the practice. If the above rules for 2 and 3 are true, then you can divide the number by 6 as well. 

For instance, if a number’s digits add up to something divisible by 3 and end in an even number, it will be divisible by 2,3, and 6. 960 divided by 3 is 320. 

Dividing by 7

This one is a little trickier and works with numbers three digits or longer, so bear with us here! To check if the number is divisible by 7, start with the last digit of the number. Double that number, then subtract the doubled number from the remaining two digits of the number. 

Here’s an example: Let’s say the number is 161. First, double the 1 to get 2. If you subtract 2 from 16, you get 14 which is divisible by 7. Therefore, we can say that 161  is divisible by 7. And when we check out work, sure enough, 161 divided by 7 is 23!

Dividing by 8

This is another division hack that works with larger numbers. If the last three digits create a number that is divisible by 8, the entire number will also be divisible by 8. As an example 9180, the last three digits - as their own number - can be divided by 8, as can 9128. 9128 divided by 8 is 1,141!

Dividing by 9

If the sum of all of the digits of the number is divisible by nine, then the number itself is divisible by nine. For instance, the sum of the number 72 is 9, and when it’s divided by nine, the answer is 8! 

Dividing by 10

Similar to the trick with dividing by five, if a number ends in a zero, then it’s divisible by 10. As a bonus, the answer dividers are looking for will exist in the number already in the hundreds, tens, and ones place. For instance, 250 divided by 10 is 25. 

Get ahead in the learning equation

After the challenges of the last school year, we know there’s a lot of pressure on parents to get kids back on track. 

Never fear, we’re here to help! 

Along with expert, personalized math tutoring in topics ranging from pre-algebra to calculus and trigonometry, we’ve got plenty of resources for kids and parents!

From math tutorials to study guides and more, check out this expertly-curated content designed to support your budding mathematician: 

A photo of Virginia

Virginia started with iD Tech at the University of Denver in 2015 and has loved every minute since then! A former teacher by trade, she has a master's in education and loves working to embolden the next generation through STEM. Outside the office, you can usually find her reading a good book, struggling on a yoga mat, or exploring the Rocky Mountains.