Division & RulesBy: Ashley Younts

Using the divisibility rules:

For each number there is a rule that will help you learn what numbers are divisible by.

Stick to the rules!

If the last digit is even, the original number is divisible by two.

Divisibility by 2

……

Example: 916 would be divisible by two because “6” is an even number.

817 wouldn't work because “7” is not an even number.

If the sum of the digits is divisible by 3, then the original number is divisible by 3.

DIVISIBILITY BY 3

2+1+6=9

Example: 216

9 is divisible by 3

would not work because 2+1+5=8

8 is not divisible by 3.

215

215

If the last two digits form a number that is divisible by 4, then the original number is divisible by 4.

Divisibility by 4

4324 & 4325

Looking at the last two digits (underlined) you can see which one will be divisible by 4.

Example:

If the last digit is either 0 or 5, then the original number is divisible by 5.

Divisibility by 5

Example: 455 works for this one because the last digit is a 5.

Even choosing a huge number like, [893,752,075,983] it will not work, because the last digit is a 3.

If the number is divisible by 2 and 3, then it is divisible by 6.

Divisibility by 6

Example: looking at the number 1536, using the rules for both 2 and 3 we see that it checks in both:

2: if the last digit is an even number √ yes

3: add 1+5+3+6=15 √ yes

Now taking a number like 1537, we already know that it will not work because the last digit is not an even number.

We have to check both rules for 2 and three because sometimes one will check and the other will not & if one rules fails, you will automatically know that it isn’t going to work.

If one rule doesn’t work…

If the last three numbers are divisible by 8, then the original number is divisible by 8.

Divisibility by 8

8/328= 41 so this number is divisible by 8.

If the number would have had a remainder then the number would not work.

Example: 1328

If the sum of the digits is divisible by 9, then the number is divisible by 9.

Divisibility by 9

Example: 216, 2+1+6=9.

217 would not work because 2+1+7=10 and 10 is not divisible by 9.

Pay close attention, this rule is tricky!

Find the sum of the odd numbered digits, and subtract that number from the sum of the even number digits.

Divisibility by 11

7+8+0+7=22 & 5+4+2=11

22-11=11

So this number is divisible by 11.

Example: 7,204,857

If the number is divisible by 3 and 4, then it is divisible by 12.

Divisibility by 12

Example: 3156

3: 3+1+5+6= 15 which is divisible by 3… check4: last two digits are divisible by 4

This number is divisible by 12.

Now that you have learned some great rules for divisibility, it will make it easier and help take up less time when figuring out if it is divisible by certain numbers.

Ending!

Thanks to Google Images and Clip art!