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anirudhbhalotia
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P.S. - Got this question from GMAT Hacks. Sharing it here with the answer and explanation as I found it really simply explained how to tackle such concepts in general.
How many different positive integers are factors of 378 ?
(A) 10
(B) 12
(C) 16
(D) 18
(E) 24
Answer with Explanation -
[spoiler]
Answer: C
Start by finding the prime factorization of 378:
378 = 2(189)
= 2(9)(21)
= 2(3)(3)(3)(7)
= (2^1)(3^3)(7^1)
The fastest way to find the number of factors of a large number is to take the exponent of each of the prime factors, raise it by one, and multiply them all together. In this case, the exponents are 1, 3, and 1. Raise them each by one, and you have 2, 4, and 2. Multiply them all together, and the result is 2(4)(2) = 16, choice (C)[/spoiler]
How many different positive integers are factors of 378 ?
(A) 10
(B) 12
(C) 16
(D) 18
(E) 24
Answer with Explanation -
[spoiler]
Answer: C
Start by finding the prime factorization of 378:
378 = 2(189)
= 2(9)(21)
= 2(3)(3)(3)(7)
= (2^1)(3^3)(7^1)
The fastest way to find the number of factors of a large number is to take the exponent of each of the prime factors, raise it by one, and multiply them all together. In this case, the exponents are 1, 3, and 1. Raise them each by one, and you have 2, 4, and 2. Multiply them all together, and the result is 2(4)(2) = 16, choice (C)[/spoiler]
