For Students in Special Education – Divisibility Tricks

Is your teen rusty doing math “by hand”? That term sounds so old-fashioned these days, doesn’t it?. After all, when was the last time we did math without a calculator? Perhaps it was when we were learning long division and multiplication with several digits back in elementary school. After that, I believe most students are allowed to use calculators.

So, what is the upshot of all this calculator use? It seems that long division “by hand” is a skill that falls by the wayside by the time students enter high school.

Why should this matter?

Well, for one, many colleges prohibit the use of calculators on their placement exams. Students accustomed to using calculators since grade school are blindsided by tests that require them to solve math problems, especially those involving long division, without the use of a calculator. The result is that many students place into developmental math, where they must re-learn all of the four basic operations-no calculator allowed.

Reviewing the long division process while in high school, as well as committing these simple divisibility tricks to memory, can help take the sting out of long division.

Numbers Divisible by 2

Numbers are divisible by 2 if the ones digit is evenly divisible by 2.

This means that even numbers are divisible by 2.

Numbers Divisible by 3

Numbers are divisible by 3 if the sum of all the individual digits is divisible by 3.

For example, the sum of the digits for the number 3627 is 18, which is divisible by 3. Therefore, the number 3627 is evenly divisible by 3.

Numbers Divisible by 4

Whole numbers are divisible by 4 if the number formed by the last two individual digits is divisible by 4.

For example, the number formed by the last two digits of the number 3628 is 28, which is evenly divisible by 4. Therefore, 3628 is evenly divisible by 4.

Numbers Divisible by 5

Numbers are evenly divisible by 5 if the last digit of the number is 0 or 5.

Numbers Divisible by 6

Numbers are evenly divisible by 6 if they are evenly divisible by both 2 AND 3 (see rules above).

Numbers Divisible by 7

To determine if a number is divisible by 7, take the last digit off the number, double it, and subtract the doubled number from the remaining number.

If the result is evenly divisible by 7 (e.g. 14, 7, 0, -7, etc.), then the number is divisible by seven. This may need to be repeated several times.

Example: Is 3101 evenly divisible by 7?

Take off the last digit of the number, which is 1.

Double the removed digit, so 1 becomes 2.

Then, subtract 2 from 310.

The difference is 308.

Repeat the process by taking off the 8 so 308 becomes 30.

Then, double the 8 so it becomes 16 and subtract it from 30.

The difference in 14, which is a multiple of 7.

BINGO – 3103 is divisible by 7!

Numbers Divisible by 8

Numbers are divisible by 8 if the number formed by the last three individual digits is evenly divisible by 8.

For example, the last three digits of the number 305,624 is 624, which is evenly divisible by 8, so 305,624 is evenly divisible by 8.

Numbers Divisible by 9

Numbers are divisible by 9 if the sum of all the individual digits is evenly divisible by 9.

For example, in 3627, the sum of the digits is 18, which is evenly divisible by 9.

BINGO – 3627 is divisible by 9!

Numbers divisible by 10

A number is divisible by 10 only if the last digit is zero!

In our high-tech world, where solving math problems is as easy as pressing buttons on a calculator, many students lack experience in manipulating numbers on their own. Thus, they never develop a feel for numbers, or a math “sense”.

Well before crossing the college threshold, students should practice their math facts and know them cold. They also need to be able to do all four math operations the “old-fashioned” way. Without practice, the consequences are likely to be placement in a developmental math class, where students must re-learn basic math in a 15-week college semester-not exactly the ideal scenario for someone rusty!