Question 1

下列四數中，何者與63互質？

Accepted Answer

55

Answer

119

Answer

49

Answer

87

Question 2

1~20的整數中，與30互質的數有多少個？

Accepted Answer

6

Answer

8

Answer

5

Answer

7

Question 3

下列各組數中，那一組數互質？

Accepted Answer

35、54

Answer

28、77

Answer

21、87

Answer

26、91

Question 4

下列敘述何者正確？

Accepted Answer

a、b均為質數，則a、b必互質

Answer

a、b均為合數，則a、b必不互質

Answer

a、b互質，則a、b均為質數

Answer

a、b不互質，則a、b必均不為質數

Question 5

求 $(3^2 	imes 5^3 	imes 7，2^3 	imes 5^2 	imes 7)$ = ？

Accepted Answer

$5^2 	imes 7$

Answer

$3^2 	imes 5^2 	imes 7$

Answer

$2 	imes 3 	imes 5 	imes 7$

Answer

$5^3 	imes 7$

Question 6

$7^3$、$7^4$和$7^6$的所有公因數有幾個？

Accepted Answer

4

Answer

3

Answer

6

Answer

5

Question 7

45、108、135的最小公倍數為何？

Accepted Answer

540

Answer

1080

Answer

270

Answer

810

Question 8

若有一正整數N為65、104、260三個數的公倍數，則N可能為下列何者？

Accepted Answer

1560

Answer

1300

Answer

1690

Answer

1800

Question 9

[225，375] 是 (225，375) 的多少倍？

Accepted Answer

15

Answer

45

Answer

25

Answer

75

Question 10

下列那一組數的最小公倍數為 $2^4 	imes 3 	imes 5^2 	imes 7$

Accepted Answer

$5^2$ 、$2^4 	imes 3 	imes 7$

Answer

$2^4 	imes 5$ 、$3 	imes 5 	imes 7$

Answer

$2^3 	imes 7$ 、$2 	imes 3 	imes 5^2$

Answer

$2^2 	imes 5^2$ 、$2^2 	imes 3 	imes 7$

Question 11

甲、乙、丙三人同時、同地、同方向出發，繞一周長為400公尺的操場慢跑，已知甲、乙、丙三人繞一圈操場所需的時間分別為4分鐘、5分鐘、6分鐘，則他們出發後多少分鐘才會第一次在出發點會合？

Accepted Answer

60

Answer

30

Answer

120

Answer

90

Question 12

若兩數互質，則下列敘述何者正確？

Accepted Answer

這兩數相乘必定是這兩數的最小公倍數

Answer

這兩數必定都是質數

Answer

這兩數必定是一個奇數、一個偶數

Answer

這兩數必定沒有公因數

Question 13

下列那一組的最大公因數與其它各組不同？

Accepted Answer

90，126

Answer

24，36

Answer

72，84

Answer

48，60

Question 14

若  a = 48，b = 36，則 [a，b] $\div$ (a，b) = ？

Accepted Answer

12

Answer

36

Answer

48

Answer

24

Question 15

甲、乙、丙三人，分別每6天、8天、12天去科工館一次，今天三人於週日相遇，則下次三人再度相遇於週日是幾天以後？

Accepted Answer

168

Answer

24

Answer

192

Answer

48

Question 16

三個分數 $\frac{1}{12}$、$\frac{1}{30}$、$\frac{1}{45}$分別乘以一個正整數 n 之後都變成整數，則 n 之最小值為何？

Accepted Answer

180

Answer

60

Answer

360

Answer

90

Question 17

一長方體木塊，長、寬、高分別為156公分、96公分、60公分，現在想把它切成大小相同的正方體，則最少共可切成幾塊？

Accepted Answer

520

Answer

600

Answer

470

Answer

580

Question 18

求 (28，36，48) + [20，24，30] = ？

Accepted Answer

124

Answer

144

Answer

150

Answer

132

Question 19

已知 (a，72) = 12，[a，72] = 360，則 a = ？

Accepted Answer

60

Answer

108

Answer

36

Answer

72

Question 20

在 15、26、33、35 四個整數中，去掉那一個數後，其餘任意兩數均互質？

Accepted Answer

15

Answer

35

Answer

33

Answer

26

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