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The positive integer 200 has how many factors?

This topic has 3 expert replies and 0 member replies

The positive integer 200 has how many factors?

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The positive integer 200 has how many factors?

A. 2
B. 10
C. 12
D. 15
E. 24

The OA is C .

Can someone help me with a formula for such type of questions? I would be thankful.

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GMAT/MBA Expert

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Quote:
The positive integer 200 has how many factors?

A. 2
B. 10
C. 12
D. 15
E. 24

The OA is C .

Can someone help me with a formula for such type of questions? I would be thankful.
Hi VJesus12,
Let's take a look at your question.

We are asked to find the number of factors of 200.
Let's find the number of factors of 200 step by step.

Step 1:
To find the number of factors of a number we first write the number as a product of its prime factors.
$$200=\ 2\times100$$
$$200=\ 2\times10\times10$$
$$200=\ 2\times2\times5\times2\times5$$


Step 2:
Now write the repeating factors using exponents.
$$200=\ 2^3\times5^2$$


Step 3:
Add one to each exponent and find the product. This product will be equal to the number of factors.
Therefore the number of factors of 200 will be:
$$=\left(3+1\right)\times\left(2+1\right)$$
$$=4\times3=12$$

Therefore, there are 12 factors of 200.
Hence, Option C is correct.

Hope it helps.
I am available if you'd like any follow up.

_________________
GMAT Prep From The Economist
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GMAT/MBA Expert

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VJesus12 wrote:
The positive integer 200 has how many factors?

A. 2
B. 10
C. 12
D. 15
E. 24

The OA is C .

Can someone help me with a formula for such type of questions? I would be thankful.
APPROACH #1 - FORMULA
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

Now onto the question...
Example: 200 = (2^3)(5^2)
So, the number of positive divisors of 200 = (3+1)(2+1)
= (4)(3)
= 12
= C

APPROACH #2 - LIST
We can quickly list all of the factors of 200
I suggest we do so in PAIRS of values whose product is 200
We get:
1 and 200
2 and 100
4 and 50
5 and 40
8 and 25
10 and 20
DONE!

Total = 12
= C

Cheers,
Brent

_________________
Brent Hanneson – Creator of GMATPrepNow.com
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VJesus12 wrote:
The positive integer 200 has how many factors?

A. 2
B. 10
C. 12
D. 15
E. 24
We can break 200 into primes, then add 1 to each exponent and find the product of all the sums. That product will give us the number of total factors.

200 = 20 x 10 = 2^2 x 5^1 x 2^1 x 5^1 = 2^3 x 5^2

Thus, 200 has (3 + 1)(2 + 1) = 4 x 3 = 12 factors.

Answer: C

_________________

Scott Woodbury-Stewart
Founder and CEO
scott@targettestprep.com



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