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# What is the greatest value of the positive integer p such that 2^p is

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Math Expert
Joined: 02 Sep 2009
Posts: 58382
What is the greatest value of the positive integer p such that 2^p is  [#permalink]

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01 Apr 2018, 10:36
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15% (low)

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72% (01:08) correct 28% (01:32) wrong based on 69 sessions

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What is the greatest value of the positive integer p such that 2^p is a factor of 80^50?

(A) 4
(B) 10
(C) 50
(D) 100
(E) 200

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Posts: 168
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Concentration: General Management, Marketing
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Re: What is the greatest value of the positive integer p such that 2^p is  [#permalink]

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01 Apr 2018, 10:43
Bunuel wrote:
What is the greatest value of the positive integer p such that 2^p is a factor of 80^50?

(A) 4
(B) 10
(C) 50
(D) 100
(E) 200

80^50=(2^200*5^50)

so greatest value is 200

option E
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What is the greatest value of the positive integer p such that 2^p is  [#permalink]

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Updated on: 12 Aug 2018, 03:38
Bunuel wrote:
What is the greatest value of the positive integer p such that 2^p is a factor of 80^50?

(A) 4
(B) 10
(C) 50
(D) 100
(E) 200

we are asked to find the greatest value of the positive integer p. In order to find out the greatest value of p as a exponent of base 2 we have to factorize 80^50.

$$(2*2*2*2*5)^{50}$$
=$${(2^4)^{50}*5^{50}$$
=$$(2^{200} )*5^{50}$$

so,$$2^{200}$$shows that the greatest value of p. The correct answer is E.

Originally posted by KSBGC on 06 Apr 2018, 13:39.
Last edited by KSBGC on 12 Aug 2018, 03:38, edited 4 times in total.
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What is the greatest value of the positive integer p such that 2^p is  [#permalink]

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07 Apr 2018, 12:15
Bunuel wrote:
What is the greatest value of the positive integer p such that 2^p is a factor of 80^50?

(A) 4
(B) 10
(C) 50
(D) 100
(E) 200

$$(ab)^{n} = a^{n}b^{n}$$
$$(a^{m})^{n}=a^{(m*n)}$$

Find prime factors of 80, raise to 50th power
$$80 = (2*2*2*2*5) = (2^4*5)$$
$$(2^4*5)^{50}=$$
$$(2^4)^{50}*5^{50}=$$
$$2^{200}5^{50}$$

5 to any power ends in 5. NEVER divisible by 2. The other factor of $$(80)^{50}=2^{200}$$

$$(80)^{50}=$$
$$(2^{200}*5^{50})=(2^{p}*5^{50})$$
$$2^{p}=2^{200}$$
$$p=200$$

There are 200 powers of 2 in $$(80)^{50}$$

selim , I think there is a small typo in your answer: $$5^{200}$$
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What is the greatest value of the positive integer p such that 2^p is   [#permalink] 07 Apr 2018, 12:15
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