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# The number 100^2 has how many factors?

Solved 2 Answers 581 Views
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The number 100has how many factors?

A) 28

B) 25

C) 24

D) 20

E) 16

I know i can try to solve this problem by number crunching, but is there a better techinque or formula.

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Yes there is here it goes
Number = (prime-factor1) ^ a x (prime-factor2)^2
Number of factors = (a+1)*(b+1)
for example 72 - 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, and 72. i.e. tweleve factors
72 = 2^3 * 3 ^ 2
total factors = (3 + 1) * (2 +1 ) => 12
Simarly in this questions
100^2 = (2^2 x 5 ^2) ^2  = (2^4) x (5^4)
a = 4, b = 4
= (4+1)(4+1)
= 25
answered Jun 9, 2014 by Senior Associate (475 points)
selected Jun 9, 2014
perfect thanx, exactly what is was looking for
commented Jun 9, 2014 by Partner (696 points)
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the answer is 25

answered Jun 9, 2014 by Guru (5,808 points)
obviousy i know the answer, i am looking for a better technique
commented Jun 9, 2014 by Partner (696 points)
Student Speaks Jyotsna Mehta

Indian School of Business, Co'18

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