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how many integers can be factors of 78? (do it without [#permalink ]
08 Nov 2007, 01:19

how many integers can be factors of 78? (do it without tediously listing the factors)

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bmwhype2 wrote:

how many integers can be factors of 78? (do it

without tediously listing the factors )

4

I'm not listing the factors

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1,2,3 and 13!!
Is there some "hidden" trick or "short" method behind it, if Yes, could you please explain?

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sidbidus wrote:

bmwhype2 wrote:

how many integers can be factors of 78? (do it

without tediously listing the factors )

4

I'm not listing the factors

Are you guys doping prime factorization? it is asking only factors not different prime factors. so i guess it should be 8.

1, 2, 3, 6, 13, 26, 39, 78.

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LM wrote:

1,2,3 and 13!! Is there some "hidden" trick or "short" method behind it, if Yes, could you please explain?

this is a variation of one of the Challenges.

we get the prime factors of 78:

2 *39

2* 3* 13

Now here's where it gets nice.

we look at the exponents of each of the factors and add one.

2, 2, 2

we multiply all the modified exponents together= 2*2*2=8 factors in all

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factors of 78
78 = 2 * 39
so (1+1)* (1+1) = 2*2 = 4
total four factors.

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LM wrote:

1,2,3 and 13!! Is there some "hidden" trick or "short" method behind it, if Yes, could you please explain?

http://www.gmatclub.com/forum/t55022

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bmwhype2 wrote:

how many integers can be factors of 78? (do it without tediously listing the factors)

something i have noticed, unless it is a perfect square (ex. 4 or 25) integer must have EVEN # of factors

i get 8:

1,2,3,6,13,26,39,78

using the method that bkk145's shown me:

prime factorization

2*3*13

(1+1)(1+1)(1+1) = 8

either way its 8

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bmwhype2 wrote:

how many integers can be factors of 78? (do it without tediously listing the factors)

If the prime factorization of an integer is a^n * b^m * c^p, then the number of factors that integer has = (n+1)(m+1)(p+1).

In this case that gives us 8 factors.

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GK_Gmat wrote:

bmwhype2 wrote:

how many integers can be factors of 78? (do it without tediously listing the factors)

If the prime factorization of an integer is a^n * b^m * c^p, then the number of factors that integer has = (n+1)(m+1)(p+1).

In this case that gives us 8 factors.

Perfect !

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bmwhype2 wrote:

how many integers can be factors of 78? (do it without tediously listing the factors)

Sorry, but I'm a little confused. I came across a similar problem and had trouble with your method. The question is how many positive intergers are factors of 441?

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Ant wrote:

bmwhype2 wrote:

how many integers can be factors of 78? (do it without tediously listing the factors)

Sorry, but I'm a little confused. I came across a similar problem and had trouble with your method. The question is how many positive intergers are factors of 441?

factor 441

441 | 7

63 | 3

21 | 7

3

3^2*7^2 = (2+1)*(2+1) = 9

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can someone explain this method with apples and oranges please?

I get lost after finding the prime factors.

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asdert wrote:

can someone explain this method with apples and oranges please?

I get lost after finding the prime factors.

it is very good that

a^n * b^m * c^p => Nf = (n+1)(m+1)(p+1). (a,b,c -prime numbers)

why is it correct?

one has such cases: {a^0,a^1,.......a^n}*{b^0,b^1,......b^m}*{c^0,c^1,......c^p}

therefore, for a - n+1 (from 1=a^0 to a^n)

b - m+1

c - p+1

Nf=(n+1)(m+1)(p+1)

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So, is this correct then?
Factors of 60:
60/2
30/2
15/3
5
2² * 3 * 5, therefore (2+1)(1+1(1+1) = 12
Outcome number includes 1 and itself, correct? awesome! thanks for the tip.

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asdert wrote:

So, is this correct then? Factors of 60: 60/2 30/2 15/3 5 2² * 3 * 5, therefore (2+1)(1+1(1+1) = 12 Outcome number includes 1 and itself, correct? awesome! thanks for the tip.

Yes {60,30,20,15,12,10,6,5,4,3,2,1} = 12

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Does this holds tru for any number or are there any exceptions? I've tested it on a bunch and all seem to be ok.
How come this stuff is not on any study guide?
I thought Mgmat was going to cover all this important tricks. I guess that's why the forum rocks.
Is there a thread somewhere with tips like this? (not necessarily factors related)
Thanks!

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asdert wrote:

Does this holds tru for any number or are there any exceptions? I've tested it on a bunch and all seem to be ok. How come this stuff is not on any study guide? I thought Mgmat was going to cover all this important tricks. I guess that's why the forum rocks. Is there a thread somewhere with tips like this? (not necessarily factors related) Thanks!

I think that walker gave a very good proof for this.