The positive integer k has exactly 2 positive prime factors 3 and 7. If k has a total of 6 positive factors inlcuding 1 and k what is the value of k?
1) 3 ^ 2 is a factor of k
2) 7 ^ 2 is not a factor of k
[spoiler] OA: D [/spoiler]
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cramya wrote:The positive integer k has exactly 2 positive prime factors 3 and 7. If k has a total of 6 positive factors inlcuding 1 and k what is the value of k?
1) 3 ^ 2 is a factor of k
2) 7 ^ 2 is not a factor of k
FROM STEM
K = 3^A*7^B
FROM 1
INSUFF
A = 2 OR 3 OR ...
FROM 2
B = 1
BOTH
iNSUFF
E
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parallel_chase
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total number of factors of k = 6
prime factors of k = 3,7
for total to be 6 factors there can be two cases
Case I
3^2 * 7 , no. of factors = (2+1)*(1+1) = 6
Case II
3* 7^2, no. of factors = (1+1) * (2+1) = 6
Statement I
3 ^ 2 is a factor of k, therefore, k has to be 3^2 * 7 = 63
Sufficient.
Statement II
7 ^ 2 is not a factor of k, therefore, k has to be 3^2 * 7 = 63.
Sufficient.
Hence D.
Let me know if you still have any doubts.
prime factors of k = 3,7
for total to be 6 factors there can be two cases
Case I
3^2 * 7 , no. of factors = (2+1)*(1+1) = 6
Case II
3* 7^2, no. of factors = (1+1) * (2+1) = 6
Statement I
3 ^ 2 is a factor of k, therefore, k has to be 3^2 * 7 = 63
Sufficient.
Statement II
7 ^ 2 is not a factor of k, therefore, k has to be 3^2 * 7 = 63.
Sufficient.
Hence D.
Let me know if you still have any doubts.
No rest for the Wicked....
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uttara
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Hi parallel_chase
can u explain these lines
can u explain these lines
how did u get no. of factors = (2+1)*(1+1) = 6 ??Case I
3^2 * 7 , no. of factors = (2+1)*(1+1) = 6
Case II
3* 7^2, no. of factors = (1+1) * (2+1) = 6
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parallel_chase
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- Posts: 1153
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Here is an example of how you can find no. of factors for any number.uttara wrote:Hi parallel_chase
can u explain these lines
how did u get no. of factors = (2+1)*(1+1) = 6 ??Case I
3^2 * 7 , no. of factors = (2+1)*(1+1) = 6
Case II
3* 7^2, no. of factors = (1+1) * (2+1) = 6
36 has 9 factors
Firstly prime factorize
36 = 2*2*3*3 = 2^2 * 3^2
Now only look at the powers of the prime factors.
(2+1)*(2+1) = 3*3 = 9
Similarly, if you need to find the factors of 63
63 = 3*3*7 = 3^2 * 7^1
Now again look at the powers of 3 and 7
Add 1 to both and multiply
(2+1)*(1+1) = 3*2 = 6.
Hope this helps.
No rest for the Wicked....
