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2013 AMC 10A Problem 19

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2013 AMC 10A Problem 19AMC 10 Step by Step

Name: Date: September 13, 2026

Bases & Digits · difficulty 3 of 5 · about 4 min · position P16-20

In base $10$ , the number $2013$ ends in the digit $3$ . In base $9$ , on the other hand, the same number is written as $(2676)_{9}$ and ends in the digit $6$ . For how many positive integers $b$ does the base- $b$ -representation of $2013$ end in the digit $3$ ?

A)
$6$
B)
$9$
C)
$13$
D)
$16$
E)
$18$

2013 AMC 10A Problem 19

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