It is currently 21 Oct 2017, 09:08

### 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

# Prime Factor Problem

Author Message
TAGS:

### Hide Tags

SVP
Joined: 16 Nov 2010
Posts: 1594

Kudos [?]: 592 [0], given: 36

Location: United States (IN)
Concentration: Strategy, Technology

### Show Tags

26 Dec 2010, 09:42
Hi

Could someone please help with this, I know that we can use the FTA to multiply the number of factors, but I'm unable to reckon clearly beyond that.

The number 105840 can be expressed in prime factors as 2^4 * 3^3 * 5 * 7^2
(a) How many of these factors in (excluding 1 and 105840) are divisible by 9?
(b) How many of these factors in (excluding 1 and 105840) are divisible by 4 but not by 8?

Regards,
Subhash
_________________

Formula of Life -> Achievement/Potential = k * Happiness (where k is a constant)

GMAT Club Premium Membership - big benefits and savings

Kudos [?]: 592 [0], given: 36

Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 7676

Kudos [?]: 17378 [0], given: 232

Location: Pune, India

### Show Tags

26 Dec 2010, 22:07
subhashghosh wrote:
Hi

Could someone please help with this, I know that we can use the FTA to multiply the number of factors, but I'm unable to reckon clearly beyond that.

The number 105840 can be expressed in prime factors as 2^4 * 3^3 * 5 * 7^2
(a) How many of these factors in (excluding 1 and 105840) are divisible by 9?
(b) How many of these factors in (excluding 1 and 105840) are divisible by 4 but not by 8?

Regards,
Subhash

$$N = 2^4 * 3^3 * 5 * 7^2$$

The total number of factors of N = 5*4*2*3 = 120

(a) How many of these factors in (excluding 1 and 105840) are divisible by 9?

For a factor to be divisible by 9, it should have at least two 3s. So you can take 3s in two ways (either take two 3s or three 3s)
You can take 2s in five ways, 5s in two ways and 7s in three ways.
Total such factors = 2*5*2*3 = 60 factors.
But this includes the number 105840 as a factor which we need to exclude. So total such factors = 60 - 1 = 59

(b) How many of these factors in (excluding 1 and 105840) are divisible by 4 but not by 8
For a factor to be divisible by 4 but not by 8, it should have exactly two 2s. So you can take 2s in only one way.
You can take 3s in four ways, 5s in two ways and 7s in three ways.
Total such factors = 1*4*2*3 = 24 factors. (This does not include 105840 as a factor because 105840 has four 2s, not two 2s.)

If the theory looks confusing, check out the number of factors theory:
http://www.veritasprep.com/blog/2010/12/quarter-wit-quarter-wisdom-writing-factors-of-an-ugly-number/
_________________

Karishma
Veritas Prep | GMAT Instructor
My Blog

Get started with Veritas Prep GMAT On Demand for \$199

Veritas Prep Reviews

Kudos [?]: 17378 [0], given: 232

Re: Prime Factor Problem   [#permalink] 26 Dec 2010, 22:07
Display posts from previous: Sort by

# Prime Factor Problem

 Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.