Higher June 2018 Paper 1 Q8

EdexcelHigherCurrent spec4 marksProperties of Numbers

8 \(A = 3^5 \times 5 \times 7^3\)
\(B = 2^3 \times 3 \times 7^4\)

(a)
(i) Find the Highest Common Factor (HCF) of \(A\) and \(B\).
(ii) Find the Lowest Common Multiple (LCM) of \(A\) and \(B\). (2)

\(A = 3^5 \times 5 \times 7^3\)
\(B = 2^3 \times 3 \times 7^4\)
\(C = 2^p \times 5^q \times 7^r\)

Given that

  • the HCF of \(B\) and \(C\) is \(2^3 \times 7\)
  • the LCM of \(A\) and \(C\) is \(2^4 \times 3^5 \times 5^2 \times 7^3\)
(b) find the value of \(p\), the value of \(q\) and the value of \(r\). (2)
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