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]
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What is the largest prime factor of 27^3−9^3−3^6?
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Scott@TargetTestPrep
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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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deloitte247
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$$27^3-9^3-3^6$$
$$\left(3^3\right)^3-\left(3^2\right)^3-3^6\ \ \ ----\ to\ base\ 3$$
$$3^9-3^6-3^6\ $$
$$3^6\left(3^3-1-1\right)$$
$$3^6\left(3^3-2\right)$$
$$3^6\left(27-2\right)$$
$$3^6\left(25\right)$$
$$3^6\left(5^2\right)$$
Hence, 5 is the largest prime factor
Answer = option C
$$\left(3^3\right)^3-\left(3^2\right)^3-3^6\ \ \ ----\ to\ base\ 3$$
$$3^9-3^6-3^6\ $$
$$3^6\left(3^3-1-1\right)$$
$$3^6\left(3^3-2\right)$$
$$3^6\left(27-2\right)$$
$$3^6\left(25\right)$$
$$3^6\left(5^2\right)$$
Hence, 5 is the largest prime factor
Answer = option C
