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# How many positive integers are factors of 216, inclusive of 1 and the

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Senior Manager
Joined: 29 Oct 2019
Posts: 314
How many positive integers are factors of 216, inclusive of 1 and the  [#permalink]

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20 Mar 2020, 18:45
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Question Stats:

83% (01:12) correct 17% (01:22) wrong based on 24 sessions

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How many positive integers are factors of 216, inclusive of 1 and the number itself?

(A) 9

(B) 12

(C) 16

(D) 18

(E) 24
Manager
Joined: 18 Dec 2017
Posts: 211
Re: How many positive integers are factors of 216, inclusive of 1 and the  [#permalink]

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20 Mar 2020, 19:05
216=2^3×3^3
No of factors = 4×4 =16

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Intern
Joined: 14 Jan 2020
Posts: 29
GMAT 1: 760 Q51 V41
How many positive integers are factors of 216, inclusive of 1 and the  [#permalink]

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21 Mar 2020, 00:46
2
total no of factors of integer $$n = a^x * b^y$$ where a, b are prime factors is given by $$(x+1)*(y+1)$$
$$216= 2^3 * 3^3$$ thus no of factors are $$(3+1)*(3+1)=16$$
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Joined: 04 Jan 2015
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Re: How many positive integers are factors of 216, inclusive of 1 and the  [#permalink]

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21 Mar 2020, 08:31

Solution

To find
We need to determine
• The number of positive factors of 216, including 1 and 216

Approach and Working out
Expressing 216 in terms of its prime factors, we get:
• $$216 = 8 * 27 = 2^3 * 3^3$$
• Hence, total number of factors of 216 = (3 + 1) x (3 + 1) = 4 x 4 = 16

Thus, option C is the correct answer.

Correct Answer: Option C
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Manager
Joined: 18 Dec 2017
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Re: How many positive integers are factors of 216, inclusive of 1 and the  [#permalink]

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21 Mar 2020, 18:45
What if we have to find odd factors?

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Director
Joined: 16 Jan 2019
Posts: 608
Location: India
Concentration: General Management
WE: Sales (Other)
Re: How many positive integers are factors of 216, inclusive of 1 and the  [#permalink]

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21 Mar 2020, 19:11
gurmukh wrote:
What if we have to find odd factors?

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If we need just the number of odd factors, the prime factor 2 can take only one power which is 0 and the prime factor 3 can take 4 powers which are 0,1,2 and 3

So total number of odd factors = 1*4 = 4

Total number of even factors = 16-4 = 12

Hope this helps
Re: How many positive integers are factors of 216, inclusive of 1 and the   [#permalink] 21 Mar 2020, 19:11

# How many positive integers are factors of 216, inclusive of 1 and the

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