2020 AMC 8 Problems/Problem 17

Revision as of 00:08, 18 November 2020 by Icematrix2 (talk | contribs) (Created page with "How many positive integer factors of <math>2020</math> have more than <math>3</math> factors? <math>\textbf{(A) }6 \qquad \textbf{(B) }7 \qquad \textbf{(C) }8 \qquad \textbf{...")
(diff) ← Older revision | Latest revision (diff) | Newer revision → (diff)

How many positive integer factors of $2020$ have more than $3$ factors?

$\textbf{(A) }6 \qquad \textbf{(B) }7 \qquad \textbf{(C) }8 \qquad \textbf{(D) }9 \qquad \textbf{(E) }10$

Solution

We list out the factors of $2020$: \[1, 2, 4, 5, 10, 20, 101, 202, 404, 505, 1010, 2020.\] Of these, only $1, 2, 4, 5, 101$ ($5$ of them) do not have more than $3$ factors. Therefore the answer is $\tau{2020}-5=\boxed{\textbf{(B) }7}$.

See also

2020 AMC 8 (ProblemsAnswer KeyResources)
Preceded by
Problem 16
Followed by
Problem 18
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25
All AJHSME/AMC 8 Problems and Solutions

The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. AMC logo.png