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Intern  Joined: 19 Feb 2012
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Find the number of factors of a three digit even number xyz  [#permalink]

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Difficulty:   65% (hard)

Question Stats: 62% (02:08) correct 38% (02:07) wrong based on 264 sessions

HideShow timer Statistics Find the number of factors of a three digit even number xyz where x, y and z are distinct prime numbers (2, 3 and 5)

A. 8
B. 10
C. 12
D. 16
E. 24

Originally posted by kiran882 on 04 Mar 2012, 04:29.
Last edited by Bunuel on 27 May 2013, 04:47, edited 2 times in total.
Edited the question
Math Expert V
Joined: 02 Sep 2009
Posts: 55801
Re: Find the number of factors of a three digit even number xyz  [#permalink]

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kiran882 wrote:
Find the number of factors of a three digit even number xyz where x, y and z are distinct prime numbers (2, 3 and 5)

A. 8
B. 10
C. 12
D. 16
E. 24

Since xyz is an even number then it's $$532=2^2*7*19$$ or $$352=2^5*11$$.

In either case the # of factors is 12:
For $$532=2^2*7*19$$ the # of factors will be $$(2+1)(1+1)(1+1)=12$$;
For $$352=2^5*11$$ the # of factors will be $$(5+1)(1+1)=12$$.

In case one doesn't know.
Finding the Number of Factors of an Integer

First make prime factorization of an integer $$n=a^p*b^q*c^r$$, where $$a$$, $$b$$, and $$c$$ are prime factors of $$n$$ and $$p$$, $$q$$, and $$r$$ are their powers.

The number of factors of $$n$$ will be expressed by the formula $$(p+1)(q+1)(r+1)$$. NOTE: this will include 1 and n itself.

Example: Finding the number of all factors of 450: $$450=2^1*3^2*5^2$$

Total number of factors of 450 including 1 and 450 itself is $$(1+1)*(2+1)*(2+1)=2*3*3=18$$ factors.

For more on number properties check: math-number-theory-88376.html

Hope it helps.
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Joined: 14 Dec 2011
Posts: 75
Re: Find the number of factors of a three digit even number xyz  [#permalink]

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Bunuel wrote:

Since xyz is an even number then it's $$532=2^2*7*19$$ or $$352=2^5*11$$.

In either case the # of factors is 12:
For $$532=2^2*7*19$$ the # of factors will be $$(2+1)(1+1)(1+1)=12$$;
For $$352=2^5*11$$ the # of factors will be $$(5+1)(1+1)=12$$.

Why answer cannot be E-24. We have 2 even numbers 532 and 352. Both are giving 12 as # of factors. Question asks, Find the number of factors of a three digit even number xyz ? So, Can't we consider both the even numbers ?
Math Expert V
Joined: 02 Sep 2009
Posts: 55801
Re: Find the number of factors of a three digit even number xyz  [#permalink]

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vinnik wrote:
Bunuel wrote:

Since xyz is an even number then it's $$532=2^2*7*19$$ or $$352=2^5*11$$.

In either case the # of factors is 12:
For $$532=2^2*7*19$$ the # of factors will be $$(2+1)(1+1)(1+1)=12$$;
For $$352=2^5*11$$ the # of factors will be $$(5+1)(1+1)=12$$.

Why answer cannot be E-24. We have 2 even numbers 532 and 352. Both are giving 12 as # of factors. Question asks, Find the number of factors of a three digit even number xyz ? So, Can't we consider both the even numbers ?

No. Find the number of factors of a three digit even number xyz. xyz is one number.
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Manager  G
Joined: 14 Dec 2011
Posts: 75
Re: Find the number of factors of a three digit even number xyz  [#permalink]

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Bunuel wrote:
No. Find the number of factors of a three digit even number xyz. xyz is one number.

Okay. Got it. Thanks
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Joined: 12 Aug 2015
Posts: 2609
Schools: Boston U '20 (M)
GRE 1: Q169 V154 Find the number of factors of a three digit even number xyz  [#permalink]

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Bunuel wrote:
kiran882 wrote:
Find the number of factors of a three digit even number xyz where x, y and z are distinct prime numbers (2, 3 and 5)

A. 8
B. 10
C. 12
D. 16
E. 24

Since xyz is an even number then it's $$532=2^2*7*19$$ or $$352=2^5*11$$.

In either case the # of factors is 12:
For $$532=2^2*7*19$$ the # of factors will be $$(2+1)(1+1)(1+1)=12$$;
For $$352=2^5*11$$ the # of factors will be $$(5+1)(1+1)=12$$.

In case one doesn't know.
Finding the Number of Factors of an Integer

First make prime factorization of an integer $$n=a^p*b^q*c^r$$, where $$a$$, $$b$$, and $$c$$ are prime factors of $$n$$ and $$p$$, $$q$$, and $$r$$ are their powers.

The number of factors of $$n$$ will be expressed by the formula $$(p+1)(q+1)(r+1)$$. NOTE: this will include 1 and n itself.

Example: Finding the number of all factors of 450: $$450=2^1*3^2*5^2$$

Total number of factors of 450 including 1 and 450 itself is $$(1+1)*(2+1)*(2+1)=2*3*3=18$$ factors.

For more on number properties check: math-number-theory-88376.html

Hope it helps.

Hi Bunuel.
I have a doubt in the highlighted part.

The question says -> x, y and z are distinct prime numbers (2, 3 and 5)
So shouldn't x,y,z be 2,3,5 respectively?
Why would they write x,y,z and then mention 2,3,5 against them.
Wouldn't GMAT specify the same?

Though the answer would not be affected but i guess a clarification would be helpful in similar questions.

Regards
Stone Cold.

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Joined: 09 Mar 2018
Posts: 1003
Location: India
Re: Find the number of factors of a three digit even number xyz  [#permalink]

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kiran882 wrote:
Find the number of factors of a three digit even number xyz where x, y and z are distinct prime numbers (2, 3 and 5)

A. 8
B. 10
C. 12
D. 16
E. 24

So the following numbers can be possible
235, 532, 352

Take factors of 1 of them
532 = 2*2*7*19

2^3 * 7^2 * 19^2

12

C
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Many of life's failures happen with people who do not realize how close they were to success when they gave up. Re: Find the number of factors of a three digit even number xyz   [#permalink] 01 Feb 2019, 07:03
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