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\(X\) is the largest prime number less than positive integer \(N.\) \(P\) is an integer such that \(P = X - 16.\) Also,

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by VJesus12 » Sun Aug 15, 2021 8:06 am

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\(X\) is the largest prime number less than positive integer \(N.\) \(P\) is an integer such that \(P = X - 16.\) Also, \(Z = 1\cdot 2\cdots \sqrt{P}.\) If \(N\) is the first non-zero perfect square whose tens digit and units digit are same, How many different prime factors does \(Z\) have?

A. 4
B. 5
C. 6
D. 160
E. 320

Answer: A

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Re: \(X\) is the largest prime number less than positive integer \(N.\) \(P\) is an integer such that \(P = X - 16.\) Al

by regor60 » Sun Aug 15, 2021 10:08 am
Start with the last statement.

The first perfect square unit and tens digit same is 100.

The closest prime number to 100 is 97, so X=97.

P=97-16= 81.

Z =1*2...*81^1/2

The prime factors of this are 2,3,5 and 7
A,4
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