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CAMANISHPARMAR
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I am getting 15.
4800=12*16*25
Anyone pls explain how is it 9.

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The answer is C and here is why.
4800 can be written as 12*400=12(2^4*5^2). Or 5(4+1)*3(2+1)=15 factors.
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CAMANISHPARMAR
How many factors of 4800 are divisible by 12?

A) 36
B) 18
C) 15
D) 9
E) 4

We see that 4800 = 12 x 400.

Here is the reason we rewrote 4800 as 12 x 400: Let’s pretend that 400 has only 4 factors: a, b, c, and d. Assume that none of these four factors is divisible by 12. But – as soon as we multiply each of them by 12 (which is why we factored out 12 originally), we see that each product – 12a, 12b, 12c, and 12d will indeed be divisible by 12. Thus, if we can determine the number of factors of 400, then we will know how many factors of 4800 are divisible by 12.

Let’s now determine the number of factors of 400:

400 = 4 x 100 = 2^4 x 5^2

Thus, 400 has (4 + 1)(2 + 1) = 15 factors.

Thus, 15 factors of 4800 are divisible by 12.

Answer: C
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But in this case 12 which is a factor is also divisible by 12 .. hence isnt the answer 15+1=16?
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SachinJose
But in this case 12 which is a factor is also divisible by 12 .. hence isnt the answer 15+1=16?

It is already included in 15. No need to add it again. Think over it, how? if you don't understand then feel free toa ask :-)
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Hi, I used the following approach: \(4800=2^{6}*3*5^{2}; 12=2^{2}*3\)

\(\frac{4800}{12}=\frac{2^{6}*3*5^{2}}{2^{2}*3}\)

\(=2^{4}*5^{2}\)

Number of Factors:\((4+1)*(2+1)= 15\)

I do not know if this approach works for similar problems. Can someone help me?
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JustusJPS
Hi, I used the following approach: \(4800=2^{6}*3*5^{2}; 12=2^{2}*3\)

\(\frac{4800}{12}=\frac{2^{6}*3*5^{2}}{2^{2}*3}\)

\(=2^{4}*5^{2}\)

Number of Factors:\((4+1)*(2+1)= 15\)

I do not know if this approach works for similar problems. Can someone help me?

Hi JustusJPS.
I used the same approach as above ,it works good.
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CAMANISHPARMAR
How many factors of 4800 are divisible by 12?

A) 36
B) 18
C) 15
D) 9
E) 4
4800=2^6*3*5^2 so 12=4*3 or 2^2*3 so 2^2*3(2^4*5^2) and we use prime factorization

so ( 4+1) (2+1)=15 i think this is the fastest approach.
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