SHSAT Math / Divisibility Made Easy

Knowing whether a given number can be divided cleanly by others is not just useful—it's like unlocking a little secret about math! This skill comes in handy for various tasks, whether you're factoring numbers or checking if a number is prime.

We've put together a collection of helpful divisibility rules just for you! Many of these rules might already be familiar to you. Please take a moment to focus on the ones that are new to you. You’ll find that learning them can be both fun and rewarding!

Divisibility Rules

Divisible by 2?	Last digit of number (furthest right or ones digit) is an even number	Example: 1040 Even number. Divisible by 2
Divisible by 3?	Sum of digits that make up number is divisible by 3	Example: 1040 Sum of digits is 1+0+4+0 = 5 NOT divisible by 3
Divisible by 4?	Last two digits (ones and tens place) is a two-digit number divisible by 4	Example: 1040 40 is divisible by 4. 1040 is divisible by 4
Divisible by 5?	Number ends in 0 or 5	Example: 1040 1040 is divisible by 5
Divisible by 6?	Divisible by both 2 and 3	Example: 1040 1040 is divisible by 2 but NOT divisible by 3. 1040 is NOT divisible by 6
Divisible by 7?	Rule 1: The "Double and Subtract" Rule (Best for 3-4 Digit Numbers) This is the standard rule taught in math circles, but it is not as simple and elegant as divisibility rules for other numbers. Separate the last digit from the rest of the number. Double that last digit. Subtract that doubled number from the remaining part of the number. If the result is 0 or a multiple of 7 (even a negative one), the original number is divisible by 7. Rule 2: Estimate and use anchoring technique to assess divisibility The fastest method to determine divisibility for 3-digit numbers is often just pulling out an obvious multiple of 7 that you know by heart (an "anchor") and looking at the difference.	Example A: 343 Separate the last digit: 3 (leaves you with 34) Double it: 3 X 2 = 6 Subtract: 34 - 6 = 28 Is 28 divisible by 7? Yes. So, 343 is divisible by 7 Example B: 1071 Separate the last digit: 1 (leaves you with 107) Double it: 1 X 2 = 2 Subtract: 107 - 2 = 105 Not sure if 105 works? Run the trick again on 105! Separate the last digit: 5 (leaves you with 10) Double it: 5 X 2 = 1- Subtract: 10 - 10 = 0 Result is a 0. So, 1071 is divisible by 7. Example C: 161 using Estimating and Anchoring To check 161:  You know 7 x 20 = 140 Subtract: 161 - 140 = 21 Since 21 is a multiple of 7, 161 is too.
Divisible by 8?	Last 3 digits of number (forms a 3-digit number) is divisible by 8	Example: 1040 Last three digits form 040 or 40 40 is divisible by 8 1040 is divisible by 8
Divisible by 9?	Sum of digits that form number is divisible by 9	Example: 1040 Sum of digits is 1+0+4+0 = 5 5 is NOT divisible by 9 1040 is NOT divisible by 9
Divisible by 10?	Number ends in 0	Example: 1040 1040 is divisible by 10
Divisible by 11?	Start at left-most digit. This is first digit. Subtract the next digit from first. Then, add the next digit. Alternately, subtract, and then add, until you run out of digits. If your final tally is 0 or a number divisible by 11, then the original number is divisible by 11.	Example: 1040 Digits are 1, 0, 4, 0 1 - 0 = 1 1+ 4 = 5 5 - 0 = 5 5 is not 0 or divisible by 11. 1040 is NOT divisible by 11 ANOTHER EXAMPLE: 1,358,016 Digits are 1,3,5,8,0,1,6 1 - 3 = -2 -2 + 5 = 3 3 - 8 = -5 -5 + 0 = -5 -5 - 1 = -6 -6 + 6 = 0 Final Tally is 0, so 1,358,016 is divisible by 11.
Divisible by 12?	Number must be divisible by 3 and 4	Example: 1040 40 is divisible by 4 1 +0 + 4 + 0 = 5, so NOT divisible by 3. Therefore, 1040 is NOT divisible by 12

Isn't it interesting how some divisibility rules are simpler and more elegant than others? While the rule for 7 might feel a bit tricky and cumbersome, don’t let that discourage you. With a little practice and patience, these rules will become second nature.

Putting these divisibility rules to memory can be a fun challenge. And as you practice, you’ll not only improve your math skills, but you’ll also develop a wonderful number sense that will improve your estimating and anchoring skills as well.