MathRevolution wrote:

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Math Revolution GMAT math practice question]

There are 3 ways to make the number 12 using products of two positive integers. These are 1*12, 2*6, and 3*4. In how many ways can 2700 be written as the product of two positive integers?

A. 6

B. 12

C. 15

D. 18

E. 36

To count the factors of a positive integer:

1. Prime-factorize the integer

2. Write the prime-factorization in the form \((a^p)(b^q)(c^r)\)...

3. The number of factors = \((p+1)(q+1)(r+1)\)...

\(2700 = 2^2 * 3^3 * 5^2\)

Adding 1 to each exponent and multiplying, we get:

Total number of factors = \((2+1)(3+1)(2+1) = 36\)

These 36 factors can be used to form 18 FACTOR PAIRS, as follows:

1*2700

2*1350

3*300

And so on.

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