Different numbers of both two sets of numbers

Question

If $A$ is the set containing the positive integer factors of $12$ and $B$ is the set containing the positive integer factors of $16$, how many different numbers are in both sets $A$ and $B$?

(Actually the answer says there are three different numbers but no matter how many times I count, I get that there are five. Why is the answer three?)

the intersection set has 3 elements:1,2,4. – Adelafif Jul 24 '15 at 06:49 — Adelafif, Jul 24 '15 at 06:49

score 1 · Answer 1 · answered Jul 24 '15 at 06:46

1

You misread "in both sets A and B" for "in either A or B". The former means "in $A\cap B$", while the latter means "in $A \cup B$". Besides you didn't request non-proper factors, so you have to count $1$, $12$ and $16$ as well.

So we have : \begin{gather} A = \{1,2,3,4,6,12\},\\ B = \{1,2,4,8,16\},\\ A\cap B = \{1,2,4\}.\\ \end{gather}

answered Jul 24 '15 at 06:46

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Geez I totally misunderstood the question. Thanks a lot! – Jun Jul 24 '15 at 06:57

Different numbers of both two sets of numbers

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