1. If

57873 = q · 10 + r, 0 ≤ r < 10,

then

(A) q = 57873, r = 0

(B) q = 7873, r = 5

(C) q = 5787, r = 3

(D) q = 5787, r = 0

(E) None of these

Answer: (C) q = 5787, r = 3

2. We wish to find q and r such that

176533 = q · 311 + r, 0 ≤ r < 311

The calculator says that 176533 ÷ 311 567.6302. Therefore

(A) q = 567, r = 0

(B) q = 567, r = 100

(C) q = 568, r = 196

(D) q = 567, r = 196

(E) None of these

Answer: (D) q = 567, r = 196

3. The greatest common factor of 105 and 75 is

(A) 3

(B) 5

(C) 9

(D) 15

(E) None of these

Answer: (D) 15

4. If gcf (105, 45) = 105u + 45v, then

(A) u = 1, v = −2

(B) u = 2, v = −1

(C) u = 1, v = 2

(D) u = 2, v = −2

(E) None of these

Answer: (A) u = 1, v = −2

5. The greatest common factor of 385 and 15 is

(A) 3

(B) 5

(C) 9

(D) 15

(E) None of these

Answer: (B) 5

6. If gcf (385, 15) = 385u + 15v, then

(A) u = 1, v = −25

(B) u = −1, v = 25

(C) u = 1, v = −26

(D) u = −1, v = 26

(E) None of these

Answer: (D) u = −1, v = 26

7. The greatest common factor of 4269 and 2134 is

(A) 1

(B) 3

(C) 7

(D) 11

(E) None of these

Answer: (A) 1

8.If gcf (4269, 2134) = 4269u + 2134v, then

(A) u = 1, v = −2

(B) u = −3, v = 5

(C) u = 1, v = −3

(D) u = −3, v = 4

(E) None of these

Answer: (A) u = 1, v = −2

9. The least common multiple of 15 and 35 is

(A) 30

(B) 35

(C) 45

(D) 70

(E) None of these

Answer: (E) lcm (15, 35) = 105

10. If ab = 79, 200 and gcf(a, b) = 30, then lcm(a, b) =

(A) 79200

(B) 26400

(C) 7920

(D) 2640

(E) None of these

Answer: (D) lcm(a, b) = 2640

11. If lcm(a, b) = ab, then gcf(a, b)=

(A) a

(B) b

(C) ab

(D) 1

(E) None of these

Answer: (D) 1

12. If gcf(a, b) = a, then lcm(a, b)=

(A) a

(B) b

(C) ab

(D) 1

(E) None of these

Answer: (B) b

13. If gcf(a, b) = 1, then gcf(ac, bc) =

(A) a

(B) b

(C) c

(D) abc

(E) None of these

Answer: (C) c

14. If gcf(a, b) = 1, then lcm(ac, bc)=

(A) a

(B) b

(C) c

(D) abc

(E) None of these

Answer: (D) abc

15. The prime factorization of 280 is

(E) None of these

Answer:

16. Let where gcf(210, b) = 1. Which of the following
numbers is not

a factor of a?

(A) 72

(B) 120

(C) 225

(D) 2520

(E) They are all factors of a.

Answer: (C)

17. Let where gcf(2310, b) =
1. Which one of the following numbers

is not a factor of a?

(A) 30

(B) 180

(C) 2310

(D) 3465

(E) They are all factors of a.

Answer: (E)

18. Let and
. Then gcf(a, b)=

(E) None of these

Answer:

19. Let and
Then lcm(a, b) =

(E) None of these

Answer:

20. If , which of the following numbers could not be lcm(a, b)?

(E) They all could be lcm(a, b).

Answer: (A) 2 · 3 · 5 · 7

21. If , which of the following numbers could be gcf(a, b)?

(E) None of these

Answer: (A) 2 · 3 · 5 · 7

22. The number of positive factors of 120 is?

(A) 2

(B) 4

(C) 8

(D) 16

(E) None of these

Answer: (D) 16

23. The number of positive factors of 2940 is?

(A) 16

(B) 24

(C) 36

(D) 54

(E) None of these

Answer: (C) 36

24. If , then the number of positive factors of a is

(A) 360

(B) 480

(C) 600

(D) 840

(E) None of these

Answer: (A) 360

25. If , then the number of positive factors of a is

(A) 360

(B) 480

(C) 600

(D) 840

(E) None of these

Answer: (D) 840