If $1176 = 2^{a} 3^{b} 7^{c}$ , find a, b and c.

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Solution

First find out the prime factorisation of 1176.
$\begin{matrix} 2 & 1176 \\ 2 & 588 \\ 2 & 294 \\ 3 & 147 \\ 7 & 49 \\ 7 & 7 \\ 1 \end{matrix}$

It can be observed that 1176 can be written as $2^{3} \times 3^{1} \times 7^{2}$ .
$1176 = 2^{3} 3^{1} 7^{2} = 2^{a} 3^{b} 7^{c}$
Hence, a = 3, b = 1 and c = 2.

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