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25 votes
25 votes
The number of distinct positive integral factors of $2014$ is _____________
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Best answer
44 votes
44 votes
First do prime factorization of $2014 - 2^{1} \times 19^{1} \times 53^{1}$

Now to get a factor of $2014,$ we can choose any combination of the prime factors including $0.$ i.e; $2^{0}$ and $2^{1}$ are possible and similarly for other prime factors also, there are $2$ possibilities. So, the total number of positive integral factors

$= 2 \times 2 \times 2 = 8$

(When all the powers of prime factors are $0,$ we get $1$ and when all the powers are maximum, we get the given number.)
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4 votes
4 votes
the factors are 1, 2, 19, 38, 53, 106, 1007 and 2014. So the total makes it 8 number of integral factors.
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