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The HCF and LCM of two numbers are 4 and 288 respectively. Find the numbers and how many such pairs are possible.

We know that, Product of two numbers = $\mathrm{H}.\mathrm{C}.\mathrm{F}\times \mathrm{L}.\mathrm{C}.\mathrm{M}$

Suppose other two numbers are A and B.so we can write;

$\mathrm{A}\times \mathrm{B}=4\times 288\phantom{\rule{0ex}{0ex}}\Rightarrow \mathrm{A}=\frac{4\times 288}{\mathrm{B}}$

Taking B = 32; then $\mathrm{A}=\frac{4\times 288}{32}=36$

Therefore other number is 36 if one number is 32.

So, (32 36) is one of the pair that satisfies the above conditions.

Regards.

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