## If m, p, and t are distinct positive prime numbers, then (m^3)(p)(t) has how many different positive factors greater

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### If m, p, and t are distinct positive prime numbers, then (m^3)(p)(t) has how many different positive factors greater

by BTGmoderatorDC » Thu Jan 26, 2023 4:26 am

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If m, p, and t are distinct positive prime numbers, then (m^3)(p)(t) has how many different positive factors greater than 1?

a. 8
b. 9
c. 12
d. 15
e. 27

OA D

Source: GMAT Prep

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### Re: If m, p, and t are distinct positive prime numbers, then (m^3)(p)(t) has how many different positive factors greater

by [email protected] » Fri Jan 27, 2023 10:34 am
BTGmoderatorDC wrote:
Thu Jan 26, 2023 4:26 am
If m, p, and t are distinct positive prime numbers, then (m^3)(p)(t) has how many different positive factors greater than 1?

a. 8
b. 9
c. 12
d. 15
e. 27

OA D

Source: GMAT Prep
To determine the total number of factors of a number, we can add 1 to the exponent of each distinct prime factor and multiply together the resulting numbers.

Thus, (m^3)(p)(t) = (m^3)(p^1)(t^1) has (3 + 1)(1 + 1)(1 + 1) = 4 x 2 x 2 = 16 total factors. Since 1 is one of those 16 factors, there are actually 15 different positive factors greater than 1.