A prime number, \(x\), is greater than \(95\) but less than \(101\).
State the value of \(x\).[1]
It is given that \(x\) can be expressed as a product of \(h-40\) and \(h+56\), where \(h\) is a positive integer.
Find the value of \(h\), showing your working clearly.[2]
Express \(874\,800\) as a product of its prime factors.[1]
Hence, find the largest possible integer value of \(\sqrt[3]{\frac{874\,800}{2k}}\) and the corresponding value of \(k\), where \(k\) is a positive integer.[3]
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Answer:(a)(i) \(97\) (ii) \(h=41\) (b)(i) \(874\,800=2^4\times3^7\times5^2\) (ii) largest value \(=18\), \(k=75\)