# How do you find two positive numbers whose product is 144 and whose sum is a minimum?

$12 , 12$
$144 = {2}^{4} \cdot {3}^{2}$
number of factor $= \left(4 + 1\right) \cdot \left(2 + 1\right) = 15$
$\implies 144 = 1 \cdot 144 = 2 \cdot 72 = 3 \cdot 48 = 4 \cdot 36 = 6 \cdot 24 = 8 \cdot 18 = 9 \cdot 16 = 12 \cdot 12$
Of these 12 pairs, the sum of $\left(12 \mathmr{and} 12 = 24\right)$ is the minimum.