700+ BTG PS Qs

[hja379]

2600 has how many positive divisors?

• 6
  12
  18
  24
  48

OA 24

[Night reader]

rephrase 2,600 has how many +ve factors?
perform prime factorization
2,600 (2) 1,300
1,300 (2) 650
650 (2) 325
325 (5) 65
65 (5) 13
13 (13) 1

2^3 * 5^2 *13^1 ---> (3+1)*(2+1)*(1+1)=24

answer 24

2600 has how many positive divisors?

• 6
  12
  18
  24
  48

OA 24

[GMATGuruNY]

2600 has how many positive divisors?

• 6
  12
  18
  24
  48

OA 24

To determine the number of positive factors of an integer:

1) Prime-factorize the integer
2) Add 1 to each exponent
3) Multiply

Since 2600^2 = 2³ * 5² * 13¹, we get (3+1)*(2+1)*(1+1) = 24 factors.

The correct answer is D.

Here's the reasoning. To determine how many factors can be created from 2600^2 = 2³ * 5² * 13¹, we need to determine the number of choices we have of each prime factor:

For 2, we can use 2�, 2¹, 2², or 2³, giving us 4 choices.
For 5, we can use 3�, 3¹, or 3², giving us 3 choices.
For 13, we can use 13� or 13¹, giving us 2 choices.

Multiplying our number of choices for each factor, we get 4*3*2 = 24 possible factors.

[Brent@GMATPrepNow]

2600 has how many positive divisors?

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

OA 24

--------ASIDE------------------------------
IMPORTANT: 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---------------------

2,600 has how many positive divisors?
2600 = (2^3)(5^2)(13^1)
So, the number of positive divisors of 2600 = (3+1)(2+1)(1+1)
=(4)(3)(2)
= 24
= D

Cheers,
Brent

[Scott@TargetTestPrep]

2600 has how many positive divisors?

• 6
  12
  18
  24
  48

OA 24

To determine the number of positive divisors, we factor 2,600 into primes, add 1 to the exponent of each unique prime factor, 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