Mr. Product

The product of the ages of all of Mr. Product's children is 1,408. The youngest child's age is half the oldest child's age. How many children does Mr. Product have, and how old are they?

Final Answer:

n =  3
a₁ =  8
a₂ =  11
a₃ =  16

Step-by-step explanation:

$$\begin{gathered} 1408=2\times 2\times 2\times 2\times 2\times 2\times 2\times 11=2^7\times 11 \\ 1408=(2\times 2\times 2)\times 11\times (2\times 2\times 2\times 2) \\ {a}_1=2\cdot 2\cdot 2=8 \\ {a}_2=11 \\ {a}_3=2\cdot a_1=2\cdot 8=16 \\ n=3 \\ \text{ Verifying Solution: } \\ s=a_1\cdot a_2\cdot a_3=8\cdot 11\cdot 16=1408 \end{gathered}$$

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