In how many ways can the integer 48 be expressed as a product of two

Question

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 .

GMATinsight · Accepted Answer

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)

Answer: Option C

sagar2911 · Answer

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

KS15 · Answer

48=(2^4)*3
No of factors=5*2=10
Since 48 is not a perfect square, no of ways=5
Answer C

cutegirlsimran · Answer

48 = 2^4 * 3^1

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

So there are exactly 5 pairs

mathivanan · Answer

48=2^4*3^1
the number of divisors are 5*2=10
(10/2)=5 pairs

VenoMfTw · Answer

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

saurabhsavant · Answer

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.

ScottTargetTestPrep · Answer

48 = 2^4 * 3 has (4 + 1)(1 + 1) = 10 positive factors. Since 48 is not a perfect square, we can choose any factor p of 48 to write p * 48/p, which expresses 48 as a product of two different positive integers. There are 10 choices for p, however, each possible product will correspond to exactly two values of p (for instance, p = 1 and p = 48 both correspond to the same product 1 * 48). Thus, there are 10/2 = 5 ways we can express 48 as a product of two different positive integers.

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In how many ways can the integer 48 be expressed as a product of two

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