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How many factors does 36^2 have

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How many factors does 36^2 have [#permalink] New post 18 Dec 2005, 02:06
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How many factors does 36^2 have?
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 [#permalink] New post 18 Dec 2005, 06:35
BG wrote:
36^2=6^4=2^4x3^4 or 25 factors


BG, the part in red confuses me.

How does 2^4*3^4=25?
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 [#permalink] New post 18 Dec 2005, 06:47
you simply add one to the powers of 2 and 3 >That is why 2^4 has 2,4,8,and 16 as factors but 1 is omitted.Foe Ex 16 has 5 factors- 2,4,8,16 and 1.Same for 3^4 -3,9,27,81 and 1 or 5 in total. This is a standard formula
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 [#permalink] New post 19 Dec 2005, 15:29
Yes it should be 25 if the question is asking only for the positive factors (which it likely is).
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 [#permalink] New post 19 Dec 2005, 18:13
BG wrote:
you simply add one to the powers of 2 and 3 >That is why 2^4 has 2,4,8,and 16 as factors but 1 is omitted.Foe Ex 16 has 5 factors- 2,4,8,16 and 1.Same for 3^4 -3,9,27,81 and 1 or 5 in total. This is a standard formula


so you mean add 1 to the power and multiply. 5*5 = 25?

Can you please verify how many factors does 36^2*7^2*5^2 has?
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 [#permalink] New post 19 Dec 2005, 18:50
36 = 6*6 = 3*2 * 3*2 = 3^2 * 2^2

36^2 = ((3^2)(2^2))^2 = 3^4 * 2^4

3^4 has 5 factors: 1,3,9,27,81
2^4 has 5 factors: 1,2,4,8,16

Total number of ways: 5*5 = 25
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 [#permalink] New post 19 Dec 2005, 18:53
Bhai wrote:
BG wrote:
you simply add one to the powers of 2 and 3 >That is why 2^4 has 2,4,8,and 16 as factors but 1 is omitted.Foe Ex 16 has 5 factors- 2,4,8,16 and 1.Same for 3^4 -3,9,27,81 and 1 or 5 in total. This is a standard formula


so you mean add 1 to the power and multiply. 5*5 = 25?

Can you please verify how many factors does 36^2*7^2*5^2 has?



36^2 = 3^4*2^4
7^2 = 7^2
5^2 = 5^2

So we have 2^4 * 3^4 * 7^2 * 5^2

2^4 has 5 factors: 1,2,4,8,16
3^4 has 5 factors: 1,3,9,27,81
7^2 has 3 factos: 1,7,49
5^2 has 3 factors: 1,5,25

Total number of possibilites = 5*5*3*3 = 225
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 [#permalink] New post 19 Dec 2005, 19:54
Yeah, that is the formular of getting how many factors are there.

X^A * Y^B * Z^C ---> (A+1)(B+1)(C+1) is the number of factors.
(X, Y, and Z are prime numbers)

36^2 = 2^4 * 3^4 ---> (4+1)(4+1)=25.

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 [#permalink] New post 19 Dec 2005, 20:52
36^2=(2^2*3^2)^2=2^4*3^4

No. of integers=(4+1)(4+1)=25

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 [#permalink] New post 19 Dec 2005, 22:36
Thanks BG and Wilfred. Your explanations are crystal clear.

Answer is 25.

Therefore, consider how many factors does 88^2 have?

88=8*11=2^3*11

Using your method,

2^3^2=2^6---> 7 factors
11^2---> 3 factors

7*3=21 factors.

Correct?
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 [#permalink] New post 20 Dec 2005, 00:48
GMATT73 wrote:
Thanks BG and Wilfred. Your explanations are crystal clear.

Answer is 25.

Therefore, consider how many factors does 88^2 have?

88=8*11=2^3*11

Using your method,

2^3^2=2^6---> 7 factors
11^2---> 3 factors

7*3=21 factors.

Correct?


Isn't it: 88= 8*11= 2^3*11^1, so that the factors should be 8?
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 [#permalink] New post 20 Dec 2005, 18:49
All the Robertos have done verry gud jab!

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 [#permalink] New post 20 Dec 2005, 19:07
GMATT73 wrote:
Thanks BG and Wilfred. Your explanations are crystal clear.

Answer is 25.

Therefore, consider how many factors does 88^2 have?

88=8*11=2^3*11

Using your method,

2^3^2=2^6---> 7 factors
11^2---> 3 factors

7*3=21 factors.

Correct?


I see you've got the hang of it :wink:
  [#permalink] 20 Dec 2005, 19:07
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