GMAT Club Around The World!!! How many factors of 200^2 are not

Question

How many factors of  200^2  are not multiples of 5?

A. 6
B. 7
C. 12
D. 31
E. 34

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Bunuel · Accepted Answer

Experts' Global Video Official Explanation

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02999 · Answer

Total factors =35 , factors multiple of 5 is 28 and not multiple of 5 is = 35-28=7.

ElninoEffect · Answer

Prime Factorisation of 200 will give us = 5^2*2^3
So prime factorisation of 200^2 will give us = (5^2*2^3)^2 = 5^4*2^6
Total factors = 5*7 = 35
Factors that are multiples of 5 = (from 2)7*4(from 5) = 28
Factors not multiples of 5 = total - factors of 5 = 35-28 = 7   B

gmatophobia · Answer

200 =   2 ^ {3} * 5 {2}

The factors are {  2 ^ {0} , 2 ^{1} , 2^{2}, 2^{3}  }, {  5 ^ {0} , 5 ^{1} , 5^{2} }

We do not want any factors of 5, hence the available factors are

{  2 ^ {0} , 2 ^{1} , 2^{2}, 2^{3} , 5 ^ {0}   }

We need to choose at least one out of the given six possible numbers

2^{1} - 1  = 31

IMO D

100mitra · Answer

Factors of 200^2 = 40,000

1, 2, 4, 5, 8, 10, 16, 20, 25, 32, 40, 50, 64, 80, 100, 
125, 160, 200, 250, 320, 400, 500, 625, 800, 1000, 
1250, 1600, 2000, 2500, 4000, 5000, 8000, 10000, 20000

Not multiple of 5 are 1, 2, 4, 8, 16, 32, 64 = 7

Shane04 · Answer

Can you explain how did you get factors that are multiples of 5 as 28?

Bunuel · Answer

200^2 = 2^6*5^4 ;

The total number of positive factors = (6 + 1)(4 + 1) = 35.
The number of factors which are NOT multiples of 5 is (6 + 1) = 7 (just ignore 5^5 to get that). 
Thus, the number of factors which are multiples of 5 is 35 - 7 = 28.

Shane04 · Answer

Thank you Bunuel! Really appreciate your quick responses.

JeffTargetTestPrep · Answer

To determine the number of positive factors, we first need to determine the prime factored form of 200^2:

200^2 =  ^2 = (2^6)(5^4)

The total number of positive factors would be:

(6 + 1)(4 + 1)

Since we are interested only in positive factors not divisible by 5, the number of such factors is:

6 + 1 = 7

Answer: B

(Note: the question stem should be changed to “How many  positive  factors of 200^2 are not multiples of 5 ?” Because, if we consider negative factors as well, the correct answer is 2 × 7 = 14, which is not among the answer choices.)

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GMAT Club Around The World!!! How many factors of 200^2 are not

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