2,600 has how many positive divisors?

Question

A. 6
B. 12
C. 18
D. 24
E. 48

Bunuel · Accepted Answer

Finding the Number of Factors of an Integer First make prime factorization of an integer n=a^p*b^q*c^r , where a , b , and c are prime factors of n and p , q , and r are their powers. The number of factors of n will be expressed by the formula (p+1)(q+1)(r+1) . NOTE: this will include 1 and n itself. Example: Finding the number of all factors of 450: 450=2^1*3^2*5^2 Total number of factors of 450 including 1 and 450 itself is (1+1)*(2+1)*(2+1)=2*3*3=18 factors. Back to the original question: If p and q are prime numbers , how many divisors does the product p^3*q^6 have? According to above the number of distinct factors of 2,600=2^3*5^2*13 would be (3+1)(2+1)(1+1)=24 . For more on this check Number Theory chapter of Math Book: math-number-theory-88376.html Hope it helps.

vgan4 · Answer

By factorization, you can write 2600 as 2600=2^3*5^2*13^1. Number of factors = (3+1)(2+1)(1+1)=24

ulm · Answer

can' t understand how we came to this. What does this multiplication mean?

ulm · Answer

Yes, thanks,
i forgot 
"The number of factors of n will be expressed by the formula  (p+1)(q+1)(r+1) "

KrishnakumarKA1 · Answer

2600 = 13 x 2^3 x 5^2

no of possible divisor = (1+1)(2+1)(3+1) = 4.3.2 = 24

Option D

Shiv2016 · Answer

2600= 26*100= 2*13*2^2*5^2
=2^3*5^2*13

Total factors= (3+1)(2+1)(1+1)= 4*3*2=24

JeffTargetTestPrep · Answer

To determine the number of positive divisors, we break 2,600 into primes, add 1 to the exponent of each unique prime, and then multiply those values together.

We see that 2,600 = 26 x 100 = 2 x 13 x 4 x 25 = 2^3 x 5^2 x 13^1.

Now we add 1 to each exponent and multiply those results:

(3 + 1)(2 + 1)(1 +1) = 24

Thus, 2,600 has 24 positive divisors.

Answer: D

BrentGMATPrepNow · Answer

If the  prime factorization  of N = (p^ a )(q^ b )(r^ c ) . . . (where p, q, r, etc are different prime numbers), then N has a total of ( a +1)( b +1)( c +1)(etc) positive divisors.

Example : 14000 = (2^ 4 )(5^ 3 )(7^ 1 )
So, the number of positive divisors of 14000 = ( 4 +1)( 3 +1)( 1 +1) =(5)(4)(2) = 40
----------ONTO THE QUESTION-------------------------

2600 = (2)(2)(2)(5)(5)(13)
= (2^ 3 )(5^ 2 )(13^ 1 )
So, the number of positive divisors of 2600 = ( 3 +1)( 2 +1)( 1 +1) =(4)(3)(2) = 24

Answer: D

Cheers,
Brent

bumpbot · Answer

Automated notice from GMAT Club BumpBot: 

A member just gave Kudos to this thread, showing it’s still useful. I’ve bumped it to the top so more people can benefit. Feel free to add your own questions or solutions.

 This post was generated automatically.

2,600 has how many positive divisors?

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Problem Solving (PS) Questions

2,600 has how many positive divisors?

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards