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# How many factors of 4800 are divisible by 12?

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Senior Manager
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How many factors of 4800 are divisible by 12?  [#permalink]

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Updated on: 05 Jun 2018, 21:37
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65% (hard)

Question Stats:

53% (01:11) correct 47% (01:57) wrong based on 129 sessions

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How many factors of 4800 are divisible by 12?

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

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Originally posted by CAMANISHPARMAR on 05 Jun 2018, 20:25.
Last edited by CAMANISHPARMAR on 05 Jun 2018, 21:37, edited 1 time in total.
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How many factors of 4800 are divisible by 12?  [#permalink]

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05 Jun 2018, 21:39
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3
tejyr wrote:
I am getting 15.
4800=12*16*25
Anyone pls explain how is it 9.

Posted from my mobile device

4800 could be written as 12 * 400
Now 10 is a factor of 400, so is 20, so is 400 itself, including many others.
10, 20 and 400 are not divisible by 12 but (12*10) and (12*20) are divisible by 12 because we are multiplying and dividing my 12.

Hence every factor of 400 is also of factor of 4800 and is divisible by 12 if we are multiplying each factor of 400 by 12.

To find the number of factors of 400 is a straightforward application of number of factors formula:-
(p+1)(q+1)(r+1)... [where p,q,r are exponents of each prime factor]

Therefore 400 can be written as $$2^4∗5^2$$
Therefore the number of factors of 400 are (4+1)(2+1) = 15 factors.

Therefore the no. of factors of 4800 which are divisible by 12 is 15 factors.

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##### General Discussion
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Re: How many factors of 4800 are divisible by 12?  [#permalink]

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05 Jun 2018, 21:15
4
I am getting 15.
4800=12*16*25
Anyone pls explain how is it 9.

Posted from my mobile device
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Re: How many factors of 4800 are divisible by 12?  [#permalink]

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11 Jun 2018, 08:25
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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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Re: How many factors of 4800 are divisible by 12?  [#permalink]

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11 Jun 2018, 08:42
1
Since we need to find factors of 4800 divisible by 12, We need to write 4800 as 12*k(some constant).

As 4800 = 12 * 400. We need to find factors of 400 which is also equal to factors of 4800 divisible by 12.

400 = 2^4 * 5 ^2. Therefore num of factors = (4+1)*(2+1) = 15
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Re: How many factors of 4800 are divisible by 12?  [#permalink]

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13 Jun 2018, 16:21
CAMANISHPARMAR wrote:
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.

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Re: How many factors of 4800 are divisible by 12?  [#permalink]

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15 Jun 2018, 23:43
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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Re: How many factors of 4800 are divisible by 12?  [#permalink]

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16 Jun 2018, 00:18
SachinJose wrote:
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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Re: How many factors of 4800 are divisible by 12?  [#permalink]

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11 Jul 2018, 21:54
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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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Re: How many factors of 4800 are divisible by 12?  [#permalink]

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11 Jul 2018, 22:23
1
JustusJPS wrote:
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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Re: How many factors of 4800 are divisible by 12? &nbs [#permalink] 11 Jul 2018, 22:23
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