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The number 10010 has how many positive integer factors?

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The number 10010 has how many positive integer factors?  [#permalink]

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New post Updated on: 11 Feb 2018, 00:04
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The number 10010 has how many positive integer factors?

A. 30
B. 32
C. 34
D. 36
E. 38

Originally posted by sxsd on 10 Feb 2018, 23:59.
Last edited by Bunuel on 11 Feb 2018, 00:04, edited 1 time in total.
Renamed the topic.
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Re: The number 10010 has how many positive integer factors?  [#permalink]

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New post 11 Feb 2018, 00:06
sxsd wrote:
The number 10010 has how many positive integer factors?

A. 30
B. 32
C. 34
D. 36
E. 38



Factorize: 10010 = 2*5*7*11*13.

Number of factors = (1 + 1)(1 + 1)(1 + 1)(1 + 1) = 32.

Answer: B.

Finding the Number of Factors of an Integer

First make prime factorization of an integer \(n=a^p*b^q*c^r\), where \(a\), \(b\), and \(c\) are prime factors of \(n\) and \(p\), \(q\), and \(r\) are their powers.

The number of factors of \(n\) will be expressed by the formula \((p+1)(q+1)(r+1)\). NOTE: this will include 1 and n itself.

Example: Finding the number of all factors of 450: \(450=2^1*3^2*5^2\)

Total number of factors of 450 including 1 and 450 itself is \((1+1)*(2+1)*(2+1)=2*3*3=18\) factors.
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Re: The number 10010 has how many positive integer factors?   [#permalink] 11 Feb 2018, 00:06

The number 10010 has how many positive integer factors?

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