Question

If r, s, and t are consecutive positive multiples of $3$, is rst divisible by $27,54$, or both?

• A. $27$ only
• B. $54$ only
• C. $27and54$ both
• D. None of the above.

Answer 1

The correct option is C $27and54$ both

Because r, s, and t are all multiples of $3$, the product $rst$ must have THREE $3^{\prime }s$ as factors. Additionally, at least one of the integers must be even, so the product will have a $2$ as a factor, because every other multiple of $3$ is even (for example, $3,6,9,12$, etc.). $27=3\times 3\times 3$ can be constructed from the known prime factors and is therefore a factor of the product $rst$. $54=2\times 3\times 3\times 3$ can also be constructed from the known prime factors and therefore is also factor of the product $rst$.