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If N= P^a*Q^b*R^c and let's assume Q and R are odf prime numbers

Then we know that total number of factors are : (a+1)*(b+1)*(c+1) [A]

Number of odd factors are: (b+1)* (c+1)

Number of even factors can be found in 2 ways

Option 1:

Subtracting odd number factors from total number factors. Which is [A-B]

Option 2:

a*(b+1)*(c+1) [here a is the power of even factor P]

Now coming to the problem:

84= 2^2*3*7

Applying option 1 approach:

Total number of factors:(2+1)*(1+1)*(1+1)=12
Number of odd factors: 4
Therefore, number of even factors: 12-4=8

Applying option 2 approach:

Number of even factors: 2*(1+1)*(1+1)=8

C IS THE ANSWER.

To me option 2 is quicker.

[b]Posted from my mobile device
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Logic 1:

84 = 2 * 2 * 3 * 7

Number of even factors: 2, 4, 6, 14, 24, 28, 42, 84 = 8

Answer C


Logic 2:

=> 84 = \(2^2 * 3^1 * 7^1\) = Total factors: (2 + 1) * (1 + 1) * (1 + 1) = 3 * 2 * 2 = 12

Odd factors: 1, 3, 7, 21 = 4

Even factors: 12 - 4 = 8

Answer C
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AbdulMalikVT
Number of even factors of 84?

A 2
B 4
C 8
D 10
E 12
­To find the number of even factors, we can multiply the number of odd factors by the power of 2 (not the power of 2)

ie, \(84 = 2^2*3*7\)

So, Even Factors \(= (2)(1+1)(1+1) = 8\), Answer must be (C) 8
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