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Math Expert V
Joined: 02 Sep 2009
Posts: 58367
In how many ways can the integer 48 be expressed as a product of two  [#permalink]

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Difficulty:   35% (medium)

Question Stats: 62% (00:58) correct 38% (01:10) wrong based on 215 sessions

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In how many ways can the integer 48 be expressed as a product of two different positive integers?

A. 10
B. 8
C. 5
D. 4
E. 2

Kudos for a correct solution.

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Joined: 21 May 2013
Posts: 636
Re: In how many ways can the integer 48 be expressed as a product of two  [#permalink]

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Bunuel wrote:
In how many ways can the integer 48 be expressed as a product of two different positive integers?

A. 10
B. 8
C. 5
D. 4
E. 2

Kudos for a correct solution.

48=(2^4)*3
No of factors=5*2=10
Since 48 is not a perfect square, no of ways=5
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Re: In how many ways can the integer 48 be expressed as a product of two  [#permalink]

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3
Bunuel wrote:
In how many ways can the integer 48 be expressed as a product of two different positive integers?

A. 10
B. 8
C. 5
D. 4
E. 2

Kudos for a correct solution.

Method 1: Listing all multiples since given number is small
48 = 1*48, 2*24, 3*16, 4*12, 6*8 => 5 ways

Method 2: Express given number as prime factors
48 = 6*8 = 2*3 * 2^3 = 2^4 * 3
Total number of factors = (4+1)(1+1) = 5*2 = 10
Since the given number is not a perfect square, there will be exact 5 pairs possible of the given 10 factors => 5 ways

Option C
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Re: In how many ways can the integer 48 be expressed as a product of two  [#permalink]

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48 = 2^4 * 3^1

No of factors = (4+1) (1+1) = 10

So there are exactly 5 pairs
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In how many ways can the integer 48 be expressed as a product of two  [#permalink]

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Bunuel wrote:
In how many ways can the integer 48 be expressed as a product of two different positive integers?

A. 10
B. 8
C. 5
D. 4
E. 2

Kudos for a correct solution.

CONCEPT:

The No. of ways of writing a (Non-Perfect Square) Number as product of two different Positive integers = Number of Factors /2
The No. of ways of writing a (Perfect Square) Number as product of two different Positive integers = (Number of Factors+1) /2

48 = 16x3 = 2^4*3^1

No. of Factors of 48 = (4+1)*(1+1) = 10

The No. of ways of writing a (Non-Perfect Square) 48 as product of two different Positive integers = Number of Factors /2 = 10/2 = 5

(1*48)
(2*24)
(3*16)
(4*12)
(6*8)

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Re: In how many ways can the integer 48 be expressed as a product of two  [#permalink]

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Bunuel wrote:
In how many ways can the integer 48 be expressed as a product of two different positive integers?

A. 10
B. 8
C. 5
D. 4
E. 2

Kudos for a correct solution.

48=2^4*3^1
the number of divisors are 5*2=10
(10/2)=5 pairs
Manager  B
Joined: 14 Mar 2014
Posts: 142
GMAT 1: 710 Q50 V34 Re: In how many ways can the integer 48 be expressed as a product of two  [#permalink]

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Bunuel wrote:
In how many ways can the integer 48 be expressed as a product of two different positive integers?

A. 10
B. 8
C. 5
D. 4
E. 2

Kudos for a correct solution.

IMO: C

If N = $$p_1^a * p_2 ^b * p_3^c ...$$

Then No. of factors of N = (a+1)(b+1)(c+1)....

No. of ways of representing as a product of two different positive integers(If N is not a perfect square) = Total No. of factors/2

Thus 48 = $$2^4 * 3^1$$

48 be expressed as a product of two different positive integers = (4+1)(1+1)/2
= 5
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Re: In how many ways can the integer 48 be expressed as a product of two  [#permalink]

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1
Bunuel wrote:
In how many ways can the integer 48 be expressed as a product of two different positive integers?

A. 10
B. 8
C. 5
D. 4
E. 2

Kudos for a correct solution.

IMHO:
prime factorization of 48=2x2x2x2x3
so the prob be comes in how many ways can 2,2,2,2,3 be arranged which is similar to arrangement of letters so i went via this route 5!/4!=5....Am I right...
comments requested in Ernest.
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Re: In how many ways can the integer 48 be expressed as a product of two  [#permalink]

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_________________ Re: In how many ways can the integer 48 be expressed as a product of two   [#permalink] 02 Apr 2018, 10:18
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