1. List in order all the factors of 12. 1, 2, 3, 4, 6, 12

2. List in order all the factors of 27. 1, 3, 9, 27

3. List in order all the factors of 56. 1, 2, 4, 7, 8, 14, 28, 56

4. List in order all the factors of 84. 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 84

5. State whether 89 is prime, composite, or neither. prime

6. State whether 105 is prime, composite, or neither. composite

7. State whether 117 is prime, composite, or neither.

8. State whether 97 is prime, composite, or neither. prime

9. Write which of the following numbers are factors of 1,240: 2, 3, 4, 5, 6, 8, 9, 10, or none. 2, 4, 5, 8, 10

10. Write which of the following numbers are factors of 462: 2, 3, 4, 5, 6, 8, 9, 10, or none. 2, 3, 6

11. Write which of the following numbers are factors of 725: 2, 3, 4, 5, 6, 8, 9, 10, or none. 5 5

12. Write which of the following numbers are factors of 239: 2, 3, 4, 5, 6, 8, 9, 10, or none. none

13. State the Fundamental Theorem of Arithmetic.

14. Write the prime factorization of 58. 2 29

15. Write the prime factorization of 60. 2 2 3 5

16. Write the prime factorization of 252. 2 2 3 2 7

17. Write the prime factorization of 88. 2 3 11

18. Write the prime factorization of 975. 3 5 2 13

19. Write the prime factorization of 315. 3 2 5 7

20. Find the greatest common factor of 18 and 70. 2 2

21. Find the greatest common factor of 126 and 90. 18

22. Find the greatest common factor of 75 and 270. 15

23. Find the greatest common factor of 33 and 70. 1 1

24. Are 165 and 54 relatively prime? no

25. Are 21 and 130 relatively prime? yes

26. Find the least common multiple of 15 and 33. 165

27. Find the least common multiple of 72 and 123. 2,952

28. Find the least common multiple of 2 and 18. 18

29. Find the least common multiple of 40 and 75. 600

30. Find the least common multiple and greatest common factor of 270 and 42. Find the product of 270 and 42. 11,340 Find the product of the LCM and GCF. 11,340 What do you notice?

31. State the definition of an arithmetic sequence.

32. State the definition of a geometric sequence.

33. State the difference between a recursive definition and an explicit definition.

34. Write the first five terms of the sequence in which a 1 = 6 and d = 3. 6, 9, 12, 15, 18

35. Write the first five terms of the sequence in which a 1 = –8 and r = –2. –8, 16, –32, 64, –128

36. Write the first five terms of the recursively defined sequence in which a 1 = – 4 and a n = a n – 1 – 3. – 4, – 7, –10, –13, –16

37. Write the first five terms of the recursively defined sequence in which a 1 = 1 and a n = 2a n – 1. 1, 2, 4, 8, 16

38. Write the first five terms of the explicitly defined sequence in which a n = 4n + 2. 6, 10, 14, 18, 22

39. Write the first five terms of the explicitly defined sequence in which a n = 2(– 3) n – 1. 2, – 6, 18, – 54, 162

40. Write the recursive definition for the sequence 2, 6, 10, 14, 18, … a 1 = 2; a n = a n – 1 + 4

41. Write the recursive definition for the sequence 9, 18, 36, 72, 144, … a 1 = 9; a n = 2a n – 1

42. Write the simplified form of the explicit formula for the sequence 4, 8, 12, 16, 20,... a n = 4n

43. Write the simplified form of the explicit formula for the sequence 9, 18, 36, 72, 144,... a n = 9(2) n – 1

44. Write 13 5 in base 10. 8 8

45. Write 15 in base 2. 1111 2

46. Write 2,776 in base 16. AD8 16

47. 1111 2 + 1010 2 11001 2

48. 431 5 – 341 5 40 5

49. 753 8 – 267 8 464 8

50. State the mathematical significance of Daniel 9:24.