Find all School-related info fast with the new School-Specific MBA Forum

 It is currently 27 Sep 2016, 13:49

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

# Properties of divisible numbers

Author Message
TAGS:

### Hide Tags

Manager
Joined: 25 May 2009
Posts: 144
Concentration: Finance
GMAT Date: 12-16-2011
Followers: 3

Kudos [?]: 100 [10] , given: 2

### Show Tags

19 Jun 2009, 20:30
10
KUDOS
4
This post was
BOOKMARKED
Here is a list of divisible number properties.

To find if number x is divisible by:
2: If x is even, True
3: If the sum of the digits of x are a multiple of 3, True
4: If the ones and tens digits form a number that is divisible by 4, True
5: If the ones digit is a 0 or 5, True
6: If x is divisible by 2 AND 3, True
7: Double the ones digit and subtract the last number from the remaining digits. If difference divisible by 7, True
8: If last 3 digits form a number that is divisible by 8, True OR If x is divisible by 2 three times, True
9: If the sum of the digits are a multiple of 9, True
10: If the ones digit is 0, True
11 (Method 1): Add each digit using these properties: - + - +... If the resulting number is divisible by 11, True
11 (Method 2): Starting with ones digit, add every other number (A). Add the remaining numbers (B). If A - B is divisible by 11, True
12: If sum of the digits is a multiple of 3 and the last two digits are a multiple of 4, True
15: If x is divisible by 3 AND 5, True

4 Example: Is 312 divisible by 4?
If the ones and tens digits form a number that is divisible by 4 then true. The ones and tens digits form 12 and 12 is divisible by 4, therefore true.

7 Example: Is 357 divisible by 7?
Double the ones digit (7) to get 14. Subtract 14 from remaining digits (35) to get 21. 21 is divisible by 7, therefore true.

9 Example: Is 95,301 divisible by 9?
The number 95,301 is divisible by 9 because the digits add to 18 (9+5+3+0+1), which is a multiple of 9.

11 (Method 1) Example: Is 824,472 divisible by 11?
-8 + 2 - 4 + 4 - 7 + 2 = -11, which is divisible by 11, therefore 824,472 is divisible by 11.

11 (Method 2) Example: Is 824,472 divisible by 11?
Starting with the units digit, add every other number:2 + 4 + 2 = 8. Then add the remaining numbers: 7 + 4 + 8 = 19. Since the difference between these two sums is 11, which is divisible by 11, 824472 is divisible by 11.

If anyone knows any other divisible number properties, please list them. Thanks.

Last edited by I3igDmsu on 28 Feb 2010, 19:30, edited 15 times in total.
GMAT Club team member
Joined: 16 Mar 2009
Posts: 115
Location: Bologna, Italy
Followers: 48

Kudos [?]: 807 [0], given: 19

Re: Properties of divisible numbers [#permalink]

### Show Tags

20 Jun 2009, 04:35
Great initiative!

You might be interested in these two posts from Basic Mathematical principles
basic-mathematical-principles-14576.html?view-post=90425#p90425
basic-mathematical-principles-14576.html?view-post=154753#p154753

Keep it up! I would love to see a compilation on divisibility rules!
_________________

My Recent Posts:
All GMAT CAT Practice Tests - links, prices, reviews
Review: GMATPrep (GMAT Prep) & PowerPrep (Power Prep) Tests

Manager
Joined: 25 May 2009
Posts: 144
Concentration: Finance
GMAT Date: 12-16-2011
Followers: 3

Kudos [?]: 100 [0], given: 2

Re: Properties of divisible numbers [#permalink]

### Show Tags

20 Jun 2009, 11:59
Thanks, I added a few more.
GMAT Tutor
Joined: 24 Jun 2008
Posts: 1183
Followers: 400

Kudos [?]: 1411 [0], given: 4

Re: Properties of divisible numbers [#permalink]

### Show Tags

21 Jun 2009, 10:54
I3igDmsu wrote:
2: If x is even, True (excludes x = 0)

There's no reason to exclude 0. Zero is definitely divisible by 2;

I3igDmsu wrote:
4: If the ones and tens digits of x are divisible by 4, True

You mean: if the tens and ones digits form a number which is divisible by 4. The number 31,212 is divisible by 4, for example, because the last two digits form a number (12) which is divisible by 4, even though the tens digit and the ones digit are not individually divisible by 4.

I3igDmsu wrote:
5: If the ones digit is a 0 or 5, True (excludes x = 0)

There's no reason to exclude 0. Zero is definitely divisible by 5;

I3igDmsu wrote:
8: If last 3 digits are divisible by 8, True OR If x is divisible by 2 three times, True

Again for clarity - the last three digits should form a number divisible by 8. For example, 85,328 is divisible by 8 because 328 is divisible by 8 (328 = 8*41).

I3igDmsu wrote:
9: If the sum of the digits are 9, True

You mean: If the sum of the digits is a multiple of 9. The sum does not need to equal 9. The number 95,301 is divisible by 9, for example, because the digits add to 18, which is a multiple of 9.

I3igDmsu wrote:
10: If the ones digit is 0, True (excludes x=0)

There's no reason to exclude 0. Zero is definitely divisible by 10;
_________________

GMAT Tutor in Toronto

If you are looking for online GMAT math tutoring, or if you are interested in buying my advanced Quant books and problem sets, please contact me at ianstewartgmat at gmail.com

Manager
Joined: 25 May 2009
Posts: 144
Concentration: Finance
GMAT Date: 12-16-2011
Followers: 3

Kudos [?]: 100 [0], given: 2

Re: Properties of divisible numbers [#permalink]

### Show Tags

29 Jun 2009, 06:46
IanStewart - great comments. I've updated everything above.
Founder
Affiliations: AS - Gold, HH-Diamond
Joined: 04 Dec 2002
Posts: 14022
Location: United States (WA)
GMAT 1: 750 Q49 V42
GPA: 3.5
Followers: 3546

Kudos [?]: 21255 [0], given: 4358

Re: Properties of divisible numbers [#permalink]

### Show Tags

03 Jul 2009, 07:49
Thanks! Kudos

_________________

Founder of GMAT Club

US News 2008 - 2017 Rankings progression - New!
Just starting out with GMAT? Start here...
Need GMAT Book Recommendations? Best GMAT Books

Co-author of the GMAT Club tests

GMAT Club Premium Membership - big benefits and savings

Intern
Joined: 02 Feb 2010
Posts: 2
Followers: 0

Kudos [?]: 0 [0], given: 0

Re: Properties of divisible numbers [#permalink]

### Show Tags

02 Feb 2010, 16:39
Quote:

11 Example: Is 824,472 divisible by 11?
Starting with the units digit, add every other number:2 + 4 + 2 = 8. Then add the remaining numbers: 7 + 4 + 8 = 19. Since the difference between these two sums is 11, which is divisible by 11, 824472 is divisible by 11.

If anyone knows any other divisible number properties, please list them. Thanks.

Ok there's maybe one little simplification for the divisibility of number 11:

There's one scheme applied to the digits : - + - + etc. if the forming number is divisible by 11 then our number is divisible by 11.

Lets take for ex 3916 which is divisible by 11.
Application : -3 + 9 - 1 + 6 = 11 -----> so 3916 is divisible by 11.

Another example. 1099989

-1+0-9+9-9+8-9 = -11 --------. so 1099989 is divisible by 11.

Hope it helps.

Eddie
Manager
Joined: 03 Jun 2010
Posts: 108
Followers: 2

Kudos [?]: 6 [0], given: 0

Re: Properties of divisible numbers [#permalink]

### Show Tags

24 Jun 2010, 17:48
Thanks ! It helps a lot
Manager
Joined: 14 Jun 2010
Posts: 55
Followers: 0

Kudos [?]: 1 [0], given: 10

Re: Properties of divisible numbers [#permalink]

### Show Tags

27 Jun 2010, 21:24
7: Double the ones digit and subtract the last number from the remaining digits. If difference divisible by 7, True

I cannot for the life of me figure out how this works. Would anybody be kind enough to break this methodology down with a specific example so I can see what I'm doing wrong?

Thank you!
Intern
Joined: 23 Jun 2010
Posts: 3
Followers: 0

Kudos [?]: 1 [1] , given: 1

Re: Properties of divisible numbers [#permalink]

### Show Tags

30 Jun 2010, 05:00
1
KUDOS
@BeeSkool
Consider the number 273 ,
if you want to apply the rule
Quote:
7: Double the ones digit and subtract the last number from the remaining digits. If difference divisible by 7, True

then you have to
- double the ones digit : 2 x 3 =6
- subtract 6 from the number formed by the remaing digits ( = 27) : 27 -6 = 21

21 is divisible by 7 => 273 is divisible too
_________________

$$Hugh$$

Manager
Joined: 14 Jun 2010
Posts: 55
Followers: 0

Kudos [?]: 1 [0], given: 10

Re: Properties of divisible numbers [#permalink]

### Show Tags

30 Jun 2010, 10:35
udini wrote:
@BeeSkool
Consider the number 273 ,
if you want to apply the rule
Quote:
7: Double the ones digit and subtract the last number from the remaining digits. If difference divisible by 7, True

then you have to
- double the ones digit : 2 x 3 =6
- subtract 6 from the number formed by the remaing digits ( = 27) : 27 -6 = 21

21 is divisible by 7 => 273 is divisible too

Awesome thanks!
Intern
Joined: 28 Jul 2010
Posts: 2
Followers: 0

Kudos [?]: 0 [0], given: 0

Re: Properties of divisible numbers [#permalink]

### Show Tags

02 Sep 2010, 09:58
amazing for 7 and 11 properties and thanks for sharing it
Intern
Status: What to know what someone's dream looks like? Observe a large pile of GMAT books. (c)
Joined: 30 Sep 2010
Posts: 28
Followers: 0

Kudos [?]: 4 [0], given: 1

Re: Properties of divisible numbers [#permalink]

### Show Tags

02 Oct 2010, 18:55
Bah my post got deleted. Thanks for the table. By the way, on page 244 Kaplan Premier they—incorrectly—state that, "...you can combine these rules above with factorization tom figure out whether a number is divisible by other numbers." the example given is that 8184 is divisible by 44 because it is divisible by (4 and 11). While this may be true in this case, it should advise that you use prime factorization.

For example, 36 is divisible by both 4 and 2, yet it is not divisible by 8. Rather, it should be divisible by 2 three times.

Posted from GMAT ToolKit
Intern
Joined: 22 Jun 2010
Posts: 15
Location: Dominican Republic
Schools: Rochester Institute of Technology
Followers: 0

Kudos [?]: 0 [0], given: 4

Re: Properties of divisible numbers [#permalink]

### Show Tags

06 Oct 2010, 12:25
Awesome, the MGMAT Number Properties didn't list the properties for 7,11, 12 and 15.
Senior Manager
Joined: 31 Mar 2010
Posts: 415
Location: Europe
Followers: 2

Kudos [?]: 41 [0], given: 26

Re: Properties of divisible numbers [#permalink]

### Show Tags

06 Oct 2010, 14:27
Great addition to MGMAT Number Properties.
GMAT Club Legend
Joined: 09 Sep 2013
Posts: 11704
Followers: 527

Kudos [?]: 145 [0], given: 0

Re: Properties of divisible numbers [#permalink]

### Show Tags

20 Nov 2013, 13:48
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________
GMAT Club Legend
Joined: 09 Sep 2013
Posts: 11704
Followers: 527

Kudos [?]: 145 [0], given: 0

Re: Properties of divisible numbers [#permalink]

### Show Tags

02 Feb 2016, 11:19
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________
Re: Properties of divisible numbers   [#permalink] 02 Feb 2016, 11:19
Similar topics Replies Last post
Similar
Topics:
3 Number Properties 6 06 Aug 2011, 13:31
Number Properties 2 10 Apr 2011, 19:23
number properties 6 01 Apr 2011, 01:02
1 Odd or even number PROPERTIES 6 22 Dec 2009, 15:00
2 Number properties: Prime Factors ... 11 01 Jan 2008, 14:13
Display posts from previous: Sort by