700+ BTG PS Qs

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

hja379 wrote:2600 has how many positive divisors?

• 6
  12
  18
  24
  48

OA 24

hja379 wrote: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.