How many different positive integers are factors of 441?
A) 4
B) 6
C) 7
D) 9
E) 11
How many positive factors?
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The number of positive factors follows the formula below:
if x = m^a * n^b * o^c... where m, n and o are the distinct prime factors of x, then x must have (a+1)(b+1)(c+1)... positive factors.
The answer is D. I go through the question in detail in the full solution below (taken from the GMATFix App).
-Patrick
if x = m^a * n^b * o^c... where m, n and o are the distinct prime factors of x, then x must have (a+1)(b+1)(c+1)... positive factors.
The answer is D. I go through the question in detail in the full solution below (taken from the GMATFix App).
-Patrick
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441 = 7 x 7 x 3 x 3 = (7)^2 * (3)^2
So factors = (2+1)(2+1) = 9
[spoiler]
{D}[/spoiler]
So factors = (2+1)(2+1) = 9
[spoiler]
{D}[/spoiler]
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Hi LulaBrazilia,
This type of question can be answered using a variety of approaches. Here's a method that uses Prime Factorization and a "list" of the options:
441 can be factored down in "any order"; if you can spot that it's 21x21, then great, but you can just factor it down one piece at a time...
441 = 3x147
147 = 3x49
49 = 7x7
So...
441 = 3x3x7x7
Now, let's list the factors. Every "combination" of those 4 numbers is required:
1 --->Don't forget this factor!!!! 1 is a factor of EVERYTHING
3
7
9 = 3x3
21 = 3x7
49 = 7x7
63 = 3x3x7
147 = 3x7x7
441 = 3x3x7x7
Total Factors: D
GMAT assassins aren't born, they're made,
Rich
This type of question can be answered using a variety of approaches. Here's a method that uses Prime Factorization and a "list" of the options:
441 can be factored down in "any order"; if you can spot that it's 21x21, then great, but you can just factor it down one piece at a time...
441 = 3x147
147 = 3x49
49 = 7x7
So...
441 = 3x3x7x7
Now, let's list the factors. Every "combination" of those 4 numbers is required:
1 --->Don't forget this factor!!!! 1 is a factor of EVERYTHING
3
7
9 = 3x3
21 = 3x7
49 = 7x7
63 = 3x3x7
147 = 3x7x7
441 = 3x3x7x7
Total Factors: D
GMAT assassins aren't born, they're made,
Rich
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To determine the total number of positive factors, we first break 441 into its prime factors, add 1 to each exponent and multiply the results.LulaBrazilia wrote:How many different positive integers are factors of 441?
A) 4
B) 6
C) 7
D) 9
E) 11
441 = 7^2 x 3^2
So the number of factors is (2 + 1)(2 + 1) = 3 x 3 = 9.
Answer: D
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