What is the greatest prime factor of $$49^{19}-7^{35}$$
A)2
B)3
C)7
D)13
E)19
The OA is E.
Can any expert help me with this PS question please? Thanks.
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What is the greatest prime factor...
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BTGmoderatorLU
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49¹� - 7³�LUANDATO wrote:What is the greatest prime factor of $$49^{19}-7^{35}$$
A)2
B)3
C)7
D)13
E)19
= (7²)¹� - 7³�
= 7³� - 7³�
= 7³�(7³ - 1)
= 7³�(343 - 1)
= 7³�(342)
= 7³�(9*38)
= 7³�(3*3*2*19).
The greatest prime factor is the value in blue.
The correct answer is E.
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Hi LUANDATO,What is the greatest prime factor of $$49^{19}-7^{35}$$
A)2
B)3
C)7
D)13
E)19
The OA is E.
Can any expert help me with this PS question please? Thanks.
Lets take a look at your question.
$$49^{19}-7^{35}$$
$$=\left(7^2\right)^{19}-7^{35}$$
$$=7^{38}-7^{35}$$
$$=7^{35+3}-7^{35}$$
$$=7^{35}.7^3-7^{35}$$
$$=7^{35}\ \left(7^3-1\right)$$
$$=7^{35}\ \left(343-1\right)$$
$$=7^{35}\ \left(342\right)$$
Write 342 as a product of its prime factors.
$$=7^{35}\ \left(2\times3\times3\times19\right)$$
We can see that the greatest prime factor is 19.
Therefore, Option E is correct.
Hope this helps.
I am available if you'd like any follow up.
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Scott@TargetTestPrep
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BTGmoderatorLU wrote:What is the greatest prime factor of $$49^{19}-7^{35}$$
A)2
B)3
C)7
D)13
E)19
The OA is E.
Can any expert help me with this PS question please? Thanks.
Rewriting 49^19 as (7^2)^19 or 7^38, we have:
7^38 - 7^35
7^35(7^3 - 1)
7^35(342)
7^35(19 x 18)
7^35(19 x 2 x 3^2)
Of the four prime factors (7, 19, 2, and 3), we see that 19 is the greatest.
Answer: E
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Brent@GMATPrepNow
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49^19 - 7^35 = (7^2)^19 - 7^35BTGmoderatorLU wrote:What is the greatest prime factor of $$49^{19}-7^{35}$$
A)2
B)3
C)7
D)13
E)19
The OA is E.
Can any expert help me with this PS question please? Thanks.
= 7^38 - 7^35
= (7^35)(7^3 - 1)
= (7^35)(343 - 1)
= (7^35)(342)
= (7^35)(2)(3)(3)(19)
Answer: E
Cheers,
Brent
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