If n=2^2*3^3*5^37, how many factors of n are there?

Question

If  n=2^23^35^37 , how many factors of n are there?

A. 18
B. 36
C. 54
D. 96
E. 108

Sirakri · Answer

No of factors of  a^mb^n  is  (m+1)(n+1)  where a,b are primes.
 
So, no of factors of  n=2^23^35^37 :
 (2+1)(3+1)(3+1)(1+1)=3*4*4*2=96

D.

stonecold · Answer

->Distinct Primes .

Regards
Stone Cold

0akshay0 · Answer

Number of factors of n=2^23^35^37 => (2+1)*(3+1)*(3+1)*(1+1) = 3*4*4*2 =96 Hence Option D is correct Hit Kudos if you liked is 8-)

.

BrentGMATPrepNow · Answer

Small point to make: the formula that people are using will help us determine the total number of POSITIVE divisors (factors). 
It's worth noting that -1, -2, -3, -6 etc are also factors of (2²)(3³)(5³)(7), in which case the answer is actually 192 (96 positive factors and 96 negative factors)

From the Official Guide:  If x and y are integers and x ≠ 0, then x is a divisor (factor) of y provided that y = xn for some integer n. In this case, y is also said to be divisible by x or to be a multiple of x. 
For example, 7 is a divisor or factor of 28 since 28 = (7)(4), but 8 is not a divisor of 28 since there is no integer n such that 28 = 8n.

Given that the factors of a given integer can include negative integers, the GMAT test-makers restrict the discussion to POSITIVE integers, as in "If n =(2²)(3³)(5³)(7), then how many POSITIVE factors of n are there?"

Cheers,
Brent

MathRevolution · Answer

==> The number of factors becomes (2+1)(3+1)(3+1)(1+1)=96, hence the answer is D.

Answer: D

Abhishek009 · Answer

10 sec solution....

(2+1)(3+1)(3+1)(1+1)=96 
  
Answer must be (D) 96

If n=2^23^35^37, how many factors of n are there?

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