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31 Jul 2017, 01:07
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B
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Difficulty:
5%
(low)
Question Stats:
81% (00:53) correct
19%
(01:34)
wrong
based on 160
sessions
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If n is the product of 3 same prime numbers and 1 different prime number, then how many different factors of n are there?
A. 6
B. 8
C. 9
D. 12
E. 18
A. 6
B. 8
C. 9
D. 12
E. 18
31 Jul 2017, 02:42
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If the number n can be represented as a product of 2 primes p and q,
where p has x occurrences and q has y occurrences(\(n = p^x * q^y\)),
the total number of factors possible is equal to (x+1)(y+1)
Coming back to the problem,
the prime numbers p and q occur 3 times and 1 time respectively,
the total number of factors is (1+1)(3+1) = 2*4 = 8(Option B)
where p has x occurrences and q has y occurrences(\(n = p^x * q^y\)),
the total number of factors possible is equal to (x+1)(y+1)
Coming back to the problem,
the prime numbers p and q occur 3 times and 1 time respectively,
the total number of factors is (1+1)(3+1) = 2*4 = 8(Option B)
