AMC 8 1996 Problem 1
AMC8 1996 年第 1 题
整除与因数★☆☆☆☆
How many positive factors of 36 are also multiples of 4?
36 的正因数中有多少个也是 4 的倍数？
- A.2
- B.3
- C.4
- D.5
- E.6
正确答案 · Correct Answer
B
解析 · Solution
Solution 1
The factors of 36 are 1, 2, 3, 4, 6, 9, 12, 18, and 36.
The multiples of 4 up to 36 are 4, 8, 12, 16, 20, 24, 28, 32 and 36.
Only 4, 12 and 36 appear on both lists, so the answer is 3, which is option .
. All possible factors of 36 will be here, except for ones divisible by 2 and not by 4. . Subtract factors not divisible by 4, which are 1, , and . 6-3=3, which is .
Divide 36 by 4, and the remaining factors, when multiplied by 4, will be factors of 36.
, which has 3 factors, giving us option .
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