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If n is the product of the integers from 1 to 8, inclusive

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If n is the product of the integers from 1 to 8, inclusive [#permalink] New post 09 Jul 2012, 02:31
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If n is the product of the integers from 1 to 8, inclusive, how many different prime factors greater than 1 does n have?

(A) four
(B) five
(C) six
(D) seven
(E) eight

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Question: 18
Page: 22
Difficulty: 500
[Reveal] Spoiler: OA

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Re: If n is the product of the integers from 1 to 8, inclusive [#permalink] New post 09 Jul 2012, 02:32
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SOLUTION

If n is the product of the integers from 1 to 8, inclusive, how many different prime factors greater than 1 does n have?

(A) four
(B) five
(C) six
(D) seven
(E) eight

n=8!, so it has 4 prime factors: 2, 3, 5, and 7.

Answer: A.
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Re: If n is the product of the integers from 1 to 8, inclusive [#permalink] New post 10 Jul 2012, 23:16
Difficulty Sub 550

8! has factors of 2, 3, 5 and 7 as 4 and 8 has 2 and six has 3. thus answer is A.
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Re: If n is the product of the integers from 1 to 8, inclusive [#permalink] New post 13 Jul 2012, 02:04
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SOLUTION

If n is the product of the integers from 1 to 8, inclusive, how many different prime factors greater than 1 does n have?

(A) four
(B) five
(C) six
(D) seven
(E) eight

n=8!, so it has 4 prime factors: 2, 3, 5, and 7.

Answer: A.
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Re: If n is the product of the integers from 1 to 8, inclusive [#permalink] New post 19 Jul 2012, 03:11
n = 1*2*3*4*5*6*7*8

so only Prime numbers which will be factors of n will be 2,3,5,7 (as prime numbers which are greater than 7 will not be there in the product of 1 to 8!)

So Answer is A (four)

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Re: If n is the product of the integers from 1 to 8, inclusive [#permalink] New post 25 Jul 2012, 04:46
Is it correct to say prime factors greater than 1? 1 is not a prime factor at all. If one says prime factor greater than 2, then it does make sense. Am I right in making this statement?
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Re: If n is the product of the integers from 1 to 8, inclusive [#permalink] New post 25 Aug 2012, 09:12
yep, the phrase " different prime factors greater than 1" sounds strange, since in fact, all of these primes are different.furthermore, no need to point out about 1, since 1 is not prime.
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Re: If n is the product of the integers from 1 to 8, inclusive [#permalink] New post 10 Oct 2013, 09:07
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Re: If n is the product of the integers from 1 to 8, inclusive [#permalink] New post 10 Oct 2013, 16:08
n = 8!

Prime factorization of 8!
= 1, 2, 3, 2*2, 5, 2*3, 7, 2*2*2

= 2, 3, 5, 7

= 4 prime factors > 1
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Re: If n is the product of the integers from 1 to 8, inclusive [#permalink] New post 17 Dec 2013, 08:11
8! = 1x2x3x4x5x6x7x8.. Just do prime factorization of each integer alone and then count the number of different primes in total.
Re: If n is the product of the integers from 1 to 8, inclusive   [#permalink] 17 Dec 2013, 08:11
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