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Which of the following CANNOT be the factor of (2n )(3k ), where n and
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21 Jul 2024, 22:20
21 Jul 2024, 22:20
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44% (00:56) correct
55% (00:47) wrong based on 9 sessions
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Which of the following CANNOT be the factor of \((2^n)(3^k)\), where n and k are both positive integers?
A. 8
B. 24
C. 42
D. 72
E. 162
A. 8
B. 24
C. 42
D. 72
E. 162
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Which of the following CANNOT be the factor of (2n )(3k ), where n and
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21 Jul 2024, 22:49
21 Jul 2024, 22:49
1
I think there is a problem with the question, Option A also suits the answer.
Because 8=2^3x 3^0, 0 is not a positive integer, It's a neutral integer.
In the question, it says n and k are positive integers. so, I am requesting administrators to correct the issue.
Thank you.
Because 8=2^3x 3^0, 0 is not a positive integer, It's a neutral integer.
In the question, it says n and k are positive integers. so, I am requesting administrators to correct the issue.
Thank you.
Which of the following CANNOT be the factor of (2n )(3k ), where n and
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08 Dec 2024, 09:49
08 Dec 2024, 09:49
Expert Reply
We need to check that which of the given options CANNOT be the factor of $\(\left(2^n\right)\left(3^k\right)\)$ where $n$ and $k$ are both positive integers.
The expression $\(\left(2^{\mathrm{n\right)\left(3^{\mathrm{k\right)\)$, where n and k are positive integers, can have only those factors which have only 2 's \& 3's as their prime factors.
(A) $\(8=\left(2^3\right)\)$
(B) $\(24=2^2 \times 3^1\)$
(C) $\(42=2^1 \times 3^1 \times 7^1\)$ as it is has 7 as one of the prime factors, it cannot be a factor of the given expression
(D) $\(72=2^3 \times 3^2\)$
(E) $\(162=2^1 \times 3^4\)$
Hence only (C) CANNOT be a factor of the given expression, so is the correct answer.
The expression $\(\left(2^{\mathrm{n\right)\left(3^{\mathrm{k\right)\)$, where n and k are positive integers, can have only those factors which have only 2 's \& 3's as their prime factors.
(A) $\(8=\left(2^3\right)\)$
(B) $\(24=2^2 \times 3^1\)$
(C) $\(42=2^1 \times 3^1 \times 7^1\)$ as it is has 7 as one of the prime factors, it cannot be a factor of the given expression
(D) $\(72=2^3 \times 3^2\)$
(E) $\(162=2^1 \times 3^4\)$
Hence only (C) CANNOT be a factor of the given expression, so is the correct answer.
