Vincen wrote:2,600 has how many positive divisors?

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

The OA is D.

Experts, is there a fast way to find all the divisors? Thanks.

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

Vincen wrote:2,600 has how many positive divisors?

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

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

Vincen wrote: ↑

Mon Oct 16, 2017 6:38 am

2,600 has how many positive divisors?

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

The OA is D.

Experts, is there a fast way to find all the divisors? Thanks.

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