234 and 1872 have been expressed as products of prime numbers
In "234 × 1872 = 438048", replace 234 and 1872 with their products of prime numbers

$\begin{array}{rcl} 234 \times 1872 & = & 438 048 \\ (2 \times 3^{2} \times 13) \times (2^{4} \times 3^{2} \times 13) & = & 438 048 \end{array}$

(The brackets above are not necessary but simply to show the replacement of 234 and 1872)
Apply the law of indices, that $x^{a} \times x^{b} = x^{a + b}$

$\begin{array}{rcl} 2 \times 3^{2} \times 13 \times 2^{4} \times 3^{2} \times 13 & = & 2 \times 2^{4} \times 3^{2} \times 3^{2} \times 13 \times 13 \\ = & 2^{1 + 4} \times 3^{2 + 2} \times 13^{1 + 1} \\ = & 2^{5} \times 3^{4} \times 13^{2} \end{array}$

$\begin{array}{rcl} = & 2^{5} \times 3^{4} \times 13^{2} \end{array}$ [1]

Prime Factors, HCF & LCM (Cambridge O Level Maths)

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