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Retired Moderator
Joined: 19 Nov 2020
Posts: 326
Given Kudos: 64
GRE 1: Q160 V152
If 5^a is a factor of n!, and the greatest integer value
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22 Sep 2021, 07:43
22 Sep 2021, 07:43
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If \(5^a\) is a factor of \(n!\), and the greatest integer value of \(a\) is \(6\), what is the largest possible value of \(b\) such that \(7^b\) is a factor of \(n!\) ?
(A) 2
(B) 3
(C) 4
(D) 5
(E) 6
Source: Manhattan Review, GMAT Question Bank
(A) 2
(B) 3
(C) 4
(D) 5
(E) 6
Source: Manhattan Review, GMAT Question Bank
Re: If 5^a is a factor of n!, and the greatest integer value
[#permalink]
22 Sep 2021, 10:39
22 Sep 2021, 10:39
2
motion2020 wrote:
If \(5^a\) is a factor of \(n!\), and the greatest integer value of \(a\) is \(6\), what is the largest possible value of \(b\) such that \(7^b\) is a factor of \(n!\) ?
(A) 2
(B) 3
(C) 4
(D) 5
(E) 6
(A) 2
(B) 3
(C) 4
(D) 5
(E) 6
The formula to find the powers of a prime number p in n! is \(\frac{n}{p} + \frac{n}{p^2}+\frac{n}{p^3}+..\)
So for a =6 in \(5^a\), the minimum value of n is 25 and max is 29.
And since largest possible value is asked.
\(\frac{29}{7} + \frac{29}{7^2} = 4+0 \). There are \(7^4\) as a factor in 29!.
Answer is C) 4
Retired Moderator
Joined: 19 Nov 2020
Posts: 326
Given Kudos: 64
GRE 1: Q160 V152
Re: If 5^a is a factor of n!, and the greatest integer value
[#permalink]
22 Sep 2021, 12:18
22 Sep 2021, 12:18
that's a quant craze 
GREG-MAT, I have signed into his website recently, is asking for such a craze constantly
The formula to find the powers of a prime number p in n! is \(\frac{n}{p} + \frac{n}{p^2}+\frac{n}{p^3}+..\)
So for a =6 in \(5^a\), the minimum value of n is 25 and max is 29.
And since largest possible value is asked.
\(\frac{29}{7} + \frac{29}{7^2} = 4+0 \). There are \(7^4\) as a factor in 29!.
Answer is C) 4
GREG-MAT, I have signed into his website recently, is asking for such a craze constantly
eskay1981 wrote:
motion2020 wrote:
If \(5^a\) is a factor of \(n!\), and the greatest integer value of \(a\) is \(6\), what is the largest possible value of \(b\) such that \(7^b\) is a factor of \(n!\) ?
(A) 2
(B) 3
(C) 4
(D) 5
(E) 6
(A) 2
(B) 3
(C) 4
(D) 5
(E) 6
The formula to find the powers of a prime number p in n! is \(\frac{n}{p} + \frac{n}{p^2}+\frac{n}{p^3}+..\)
So for a =6 in \(5^a\), the minimum value of n is 25 and max is 29.
And since largest possible value is asked.
\(\frac{29}{7} + \frac{29}{7^2} = 4+0 \). There are \(7^4\) as a factor in 29!.
Answer is C) 4
