AMC 8 2018 Problem 18

AMC8 2018 年第 18 题

整除与因数★★★☆☆
How many positive factors does 23,232 have?
23,232 有多少个正因子？
  1. A.9
  2. B.12
  3. C.28
  4. D.36
  5. E.42

正确答案 · Correct Answer

E

解析 · Solution

Solution 1

We can first find the prime factorization of 23,232, which is 26⋅31⋅1122^6\cdot3^1\cdot11^2. Now, we add one to our powers and multiply. Therefore, the answer is (6+1)⋅(1+1)⋅(2+1)=7⋅2⋅3=42(6+1)\cdot(1+1)\cdot(2+1)=7\cdot2\cdot3=42

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