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What is the greatest positive integer [m]x[/m] so that [m]3^x[/m] is a
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10 Mar 2021, 20:12
10 Mar 2021, 20:12
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What is the value of the greatest positive integer \(x\), such that \(3^x\) is a divisor of \(10!\)
A. 1
B. 2
C. 3
D. 4
E. 5
A. 1
B. 2
C. 3
D. 4
E. 5
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What is the greatest positive integer [m]x[/m] so that [m]3^x[/m] is a
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10 Jul 2021, 07:39
10 Jul 2021, 07:39
2
Theory: To find the power of a prime number in a factorial we need to divide the factorial (number) by all those powers of the prime number such that those powers are less than the factorial(number)
\(\frac{10}{3}\) + \(\frac{10}{3^2}\) [we stop at \(3^2\) because \(3^3\) > 10]
= 3 (take the integer just less than the decimal) + 1 = 4
So, the greatest positive integer \(x\), such that \(3^x\) is a divisor of \(10!\) will be 4
So, Answer will be D
Hope it helps!
To learn more about Remainders, watch the following video
\(\frac{10}{3}\) + \(\frac{10}{3^2}\) [we stop at \(3^2\) because \(3^3\) > 10]
= 3 (take the integer just less than the decimal) + 1 = 4
So, the greatest positive integer \(x\), such that \(3^x\) is a divisor of \(10!\) will be 4
So, Answer will be D
Hope it helps!
To learn more about Remainders, watch the following video
gmatclubot
What is the greatest positive integer [m]x[/m] so that [m]3^x[/m] is a [#permalink]
10 Jul 2021, 07:39
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