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How many positive odd factors does 768 have?

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How many positive odd factors does 768 have?  [#permalink]

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New post 11 Oct 2018, 02:43
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A
B
C
D
E

Difficulty:

  55% (hard)

Question Stats:

60% (01:16) correct 40% (01:19) wrong based on 139 sessions

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How many positive odd factors does 768 have?  [#permalink]

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New post 11 Oct 2018, 02:50
1
768 = \(2^8\)\(3^1\)

No of Odd-factors = \(2^0\)\(3^1\) = (0+1)(1+1) = 1*2 = 2.

C is the answer.
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How many positive odd factors does 768 have?  [#permalink]

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New post 11 Oct 2018, 10:18
Bunuel wrote:
How many positive odd factors does 768 have?

A. zero
B. one
C. two
D. three
E. four

To find the number of factors of an integer including itself and 1

1) prime factorize the integer:\(768=2^8*3^1\)

2) to find the number of odd factors only, use only the odd prime factor, 3. Take 3's exponent and ADD 1
\((1+1)=2\)

3) for cases in which no other exponent is in play, step 2 is the answer.

768 contains two odd factors (1 and 3)

Answer C


Different step #3 if there is more than one exponent. How many positive odd factors does 525 have? 1) \(525=3^15^27^1\)
2) Add 1 to each exponent: (2,3,2)
3) multiply those results: (2*3*2) = 12 factors of 525 including itself and 1

If \(n=a^p*b^q*c^r\)
Then the number of factors of \(n\) including \(n\) and 1 is expressed by the formula \((p+1)(q+1)(r+1)\)
See Bunuel , HERE, "Finding the Number of Factors of an Integer" (scroll down)

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Re: How many positive odd factors does 768 have?  [#permalink]

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New post 11 Oct 2018, 11:08
768 =2^8*3

So, there are only 2 odd factors i.e 1 and 3.
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Re: How many positive odd factors does 768 have?  [#permalink]

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New post 13 Oct 2018, 18:51
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Bunuel wrote:
How many positive odd factors does 768 have?

A. zero
B. one
C. two
D. three
E. four


First, let’s break 768 into its prime factors.

768 = 16 x 48 = 2^4 x 8 x 6 = 2^4 x 2^3 x 2^1 x 3^1 = 2^8 x 3^1

Thus, we see that 768 has only 2 odd factors, namely, 1 and 3.

Answer: C
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How many positive odd factors does 768 have?  [#permalink]

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New post 13 Oct 2018, 20:58
1
generis

generis wrote:
Bunuel wrote:
How many positive odd factors does 768 have?

A. zero
B. one
C. two
D. three
E. four

To find the number of factors of an integer including itself and 1

1) prime factorize the integer:\(768=2^8*3^1\)

2) to find the number of odd factors only, use only the odd prime factor, 3. Take 3's exponent and ADD 1
\((1+1)=2\)

3) for cases in which no other exponent is in play, step 2 is the answer.

768 contains two odd factors (1 and 3)

Answer C


Different step #3 if there is more than one exponent. How many positive odd factors does 525 have? 1) \(525=3^15^27^1\)
2) Add 1 to each exponent: (2,3,2)
3) multiply those results: (2*3*2) = 12 factors of 525 including 525 and itself - I believe you mean to say 1 and itself.

If \(n=a^p*b^q*c^r\)
Then the number of factors of \(n\) including \(n\) and itself is expressed by the formula \((p+1)(q+1)(r+1)\)
See Bunuel , HERE, "Finding the Number of Factors of an Integer" (scroll down)

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Re: How many positive odd factors does 768 have?  [#permalink]

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New post 14 Oct 2018, 06:11
Harshgmat wrote:
generis

generis wrote:

Different step #3 if there is more than one exponent. How many positive odd factors does 525 have? 1) \(525=3^15^27^1\)
2) Add 1 to each exponent: (2,3,2)
3) multiply those results: (2*3*2) = 12 factors of 525 including 525 and itself - I believe you mean to say 1 and itself.

If \(n=a^p*b^q*c^r\)
Then the number of factors of \(n\) including \(n\) and itself is expressed by the formula \((p+1)(q+1)(r+1)\)
See Bunuel , HERE, "Finding the Number of Factors of an Integer" (scroll down)

You are correct. Thank you! :)
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Re: How many positive odd factors does 768 have?   [#permalink] 14 Oct 2018, 06:11
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