Download Learning Divisibility Rules

Learning Divisibility Rules
Why learn them?
Divisibility by 2
Divisibility by 3
Divisibility by 4
Divisibility by 5
Divisibility by 6
Divisibility by 7
Divisibility by 8
Divisibility by 9
Divisibility by 10
Links to More
Why Learn Divisibility Rules?
How many times have you had to divide a
number over and over again by 2 or 3 to:
• find its factors and prime factors?
• do a long division problem?
• find a lowest common denominator,
or least common multiple?
Knowing quickly what you can cleanly
divide a number by will really help you do
these tasks well! This will help you
succeed on:
• Many later skills you’ll learn this year
• The CAT test
• The High School Exit Exam
So let’s get busy!
How to Get Around
This tutorial is easy to follow. Go through all of the
divisibility rules by clicking on the next page
symbol
after you have read a page. You can
go back to the previous page by clicking on the
back page symbol
. Go back to the home page
by clicking on the
symbol to find links to any
divisibility rule you want to jump to.
buttons are links to internet sites that can help
you learn or practice a skill or rule. Pink
underlined text is a link to another slide, and the
button will return you to the last slide you viewed.
The
button will get you to this page.
Divisibility by 2
Rule: All even numbers (last digit is 0, 2, 4, 6, or 8) are divisible
by two. “Divisible” means that when you divide a number by two,
there will be no remainder.
Examples: 336 is divisible by 2 because the last digit, 6, is even.
So you know you can divide 336 by 2 cleanly (no remainder). 336
may also be divisible by one or more other numbers, too!
• 2007 is not divisible by 2 because the last digit, 7, is not even.
But it may be divisible by other numbers!
Practice Link:
(then scroll down for on-line practice)
Divisibility by 3
Rule: When the sum of a number’s digits (add all the digits in the
number together) is divisible by 3, then the whole number is
divisible by 3, too!
Examples: 336 is divisible by 3 because the sum of the digits, 12,
(3 + 3 + 6) is divisible by 3. So you know you can divide 336 by 3
cleanly. We knew 336 was divisible by 2 - and it may have other
factors besides 2 and 3!
• 1314 is divisible by 3 because the sum of the digits, 9, is divisible
by 3. It may be divisible by other numbers, too!
• 1315 is not divisible by 3 because the sum of its digits, 10, is not
divisible by 3. Is is divisible by any number? Yes!
Practice Link:
(then scroll down for on-line practice)
Divisibility by 4
Rule: If the last two digits form a number which is divisible by 4,
then the whole number is divisible by 4, too. Ask me why!
Examples: 336 is divisible by 4 because the last two digits make
the number 36, and 36 is divisible by 4 (36 ÷ 4 = 9), so we know
that 336 is divisible by 4. Wow - 2, 3, and 4, too? Is 336 divisible
by any other numbers? Hmmm.
• 1314 is NOT divisible by 4 because the last two digits make 14,
and 14 is not divisible by 4. Don’t let that final 4 fool you.
• 44,442 is not divisible by 4 because 42 is not divisible by 4. Is it
divisible by any number? Yes! And here’s another one, too.
Practice Link:
(then scroll down for on-line practice)
Divisibility by 5
Rule: If the last digit of your number is either 0 or 5, the whole
number is divisible by 5. I mean, come on! 5, 10, 15, 20, 25 . . .
Examples: 315 is divisible by 5 because the last digit is 5, so we
know that 315 is divisible by 5. And yes, 315 is divisible by other
numbers, too. Here’s another.
• 1536 is NOT divisible by 5 because the last digit is neither 0 nor
5. Sum of digits doesn’t work here - only for divisibility by 3 or 9.
• 13,579,70 is divisible by 5 because it ends in zero. And that’s not
all, folks!
Practice Link:
(scroll down for on-line practice)
Divisibility by 6
Rule: If your number is divisible by both 2 and 3, then it is also
divisible by 6. Makes sense, doesn’t it?
Examples: 336 is divisible by 6 because it is divisible by 2 (its
even) and it is also divisible by 3 (sum of digits, 12, is divisible by
3). Note - the 6 on the end has nothing to do with divisibility by 6.
See the next example.
• 1436 is NOT divisible by 6. Even though it is divisible by 2
because it is even, it is not divisible by 3 (sum of digits is 14, and
14 is not divisible by 3).
Practice Link:
(then scroll down for on-line practice)
Divisibility by 7
Rule: Take off the last digit, double it, and subtract it from the
remaining number. If what you get is divisible by 7, your original
number is divisible by 7. If you have a big number, you can do this
a couple of times until you get a number you can more easily tell is
divisible by 7 or not. Weird, but it works.
Example: 1519 is divisible by 7. Take the 9 off, double it to 18,
and subtract the 18 from 151. You get 133. Hmmm - I can’t tell
yet, so do it again. Take the 3 off the end of 133, double it to 6,
and subtract the 6 from 13. You get 7, and 7 is certainly divisible
by 7 - so we know that 1519 is also divisible by 7. Note that if you
get zero for your final remaining number, then then the whole
number is divisible by 7.
• 367 is not divisible by 7. 36 - 14 = 22, and 7 won’t go into 22.
Practice Link:
(then scroll down for on-line practice)
Divisibility by 8
Rule: If the number formed by the last three digits is divisible by
8, then the whole number is divisible by 8, too. I think this one’s
not so helpful, to be honest, unless you start with a number that’s
in the thousands or higher.
Example: 62,232 is divisible by 8 because 232 is divisible by 8. I
had to go ahead and do 232 ÷ 8 by long division to find out, but it
was a little easier than doing 62,232 ÷ 8 with long division.
Practice Link:
(then scroll down for on-line practice)
Divisibility by 9
Rule: When the sum of a number’s digits (add all the digits in the
number together) is divisible by 9, then the whole number is
divisible by 9, too! This is like the divisibility rule for 3.
Examples: 336 is not divisible by 9 because the sum of the digits,
12, is not divisible by 9. (It is divisible by plenty of other numbers,
though - here’s one.)
• 46,008 is divisible by 9 because the sum of the digits, 18, is
divisible by 9. It’s also divisible by 2, by 3, by 4, by 6, and by 8!
Be sure you know why - go back if you need to!
Practice Link:
(then scroll down for on-line practice)
Divisibility by 10
Rule: If the last digit of your number is zero, the whole number is
divisible by 10. You know, 10, 20, 30, 40, 50, 60 . . .
Examples: 310 is divisible by 10 because the last digit is 0, so we
know that 310 is divisible by 10. Yes, 310 is divisible by 5, too.
• 1535 is NOT divisible by 10 because the last digit is not 0.
• 13,579,70 is divisible by 10 because it ends in zero.
Practice Link:
(scroll down for on-line practice)
Links to More Information
Click to find:
Why these rules work (have to scroll
down)
 A nice summary of these rules. Ask
to print!
 Divisibility rules up to 13!
 A cool site for all kinds of math for
this year and beyond.
