A prime number, \(x\), is greater than \(87\) but less than \(91\).
State the value of \(x\).[1]
It is given that \(x\) can be expressed as a product of \(h-31\) and \(h+57\), where \(h\) is a positive integer.
Find the value of \(h\), showing your working clearly.[2]
Express \(1\,524\,096\) as a product of its prime factors.[1]
Hence, find the largest possible integer value of \(\sqrt[3]{\frac{1\,524\,096}{2k}}\) and the corresponding value of \(k\), where \(k\) is a positive integer.[3]
Solution:
Solution locked
Sign in to view the step-by-step solution
Similar questions are unavailable for this question.
Answer:(a)(i) \(89\) (ii) \(h=32\) (b)(i) \(1\,524\,096=2^7\times3^5\times7^2\) (ii) largest value \(=12\), \(k=441\)