Question

if A is the hcf of 56 and 72,then find a pair of integral values of x and y such that A=56x+72y {no links}

Answer 1

Dear student
$$\begin{gathered} \mathrm{Given}\mathrm{numbers}72\mathrm{and}56 \\ 72=56\times 1+16...\left(1\right) \\ 56=16\times 3+8.....\left(2\right) \\ 16=8\times 2+0 \\ \mathrm{So},\mathrm{HCF}\mathrm{of}72\mathrm{and}56\mathrm{is}8 \\ \mathrm{Now},56=16\times 3+8[\mathrm{using}2] \\ 8=56-16\times 3 \\ \Rightarrow 8=56-\left(72-56\right)\times 3[\mathrm{using}1] \\ \Rightarrow 8=56-72\times 3+56\times 3 \\ \Rightarrow 8=56+56\times 3-72\times 3 \\ \Rightarrow 8=56\left(1+3\right)-72\times 3 \\ \Rightarrow 8=56\times 4-72\times 3 \\ \Rightarrow 8=56\times 4+72\times \left(-3\right) \\ \mathrm{On}\mathrm{comparing}\mathrm{with}56\mathrm{x}+72\mathrm{y},\mathrm{we}\mathrm{get}\mathrm{x}=4\mathrm{and}\mathrm{y}=-3 \end{gathered}$$
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