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What is the largest prime factor of 27^3−9^3−3^6?

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by Scott@TargetTestPrep » Wed Apr 10, 2019 4:35 pm
VJesus12 wrote:What is the largest prime factor of 27^3−9^3−3^6?

A. 2
B. 3
C. 5
D. 7
E. 11

[spoiler]OA=C[/spoiler]

Source: Veritas Prep

Simplifying we have:

3^9 - 3^6 - 3^6

3^6(3^3 - 1 - 1)

3^6(25)

3^6 x 5^2

Answer: C

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by deloitte247 » Wed Apr 17, 2019 7:56 am
$$27^3-9^3-3^6$$
$$\left(3^3\right)^3-\left(3^2\right)^3-3^6\ \ \ ----\ to\ base\ 3$$
$$3^9-3^6-3^6\ $$
$$3^6\left(3^3-1-1\right)$$
$$3^6\left(3^3-2\right)$$
$$3^6\left(27-2\right)$$
$$3^6\left(25\right)$$
$$3^6\left(5^2\right)$$
Hence, 5 is the largest prime factor

Answer = option C
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