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15 May 2024, 01:23
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If \(k\) is a positive integer and \(\sqrt{6k}\) is the greatest factor of \(k\), what is the number of positive factors of \(k\)?
A. 1
B. 2
C. 3
D. 4
E. 6
A. 1
B. 2
C. 3
D. 4
E. 6
15 May 2024, 01:23
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Official Solution:
If \(k\) is a positive integer and \(\sqrt{6k}\) is the greatest factor of \(k\), what is the number of positive factors of \(k\)?
A. 1
B. 2
C. 3
D. 4
E. 6
The greatest factor of a positive integer is the integer itself. So, we are given that \(\sqrt{6k}=k\):
Square: \(6k=k^2\);
\(k(6-k)=0\);
\(k=0\) (discard because we are given that \(k\) is a positive integer) or \(k=6\). 6 has four positive factors: 1, 2, 3, and 6.
Answer: D
If \(k\) is a positive integer and \(\sqrt{6k}\) is the greatest factor of \(k\), what is the number of positive factors of \(k\)?
A. 1
B. 2
C. 3
D. 4
E. 6
The greatest factor of a positive integer is the integer itself. So, we are given that \(\sqrt{6k}=k\):
Square: \(6k=k^2\);
\(k(6-k)=0\);
\(k=0\) (discard because we are given that \(k\) is a positive integer) or \(k=6\). 6 has four positive factors: 1, 2, 3, and 6.
Answer: D
27 Dec 2024, 13:44
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Any similar problems Bunuel? Please.
Bunuel
