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Name _____________________________
Date ___________________
Number Theory
Complete.
1.   Circle all of the numbers that are divisible by 8.
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429324814735
2.   Circle all of the numbers that are divisible by 2.
2395568841914
7674157108258

Complete each divisibility table. Write yes if the number is divisible by the given number. Write no if it is not divisible by the given number.
3.         76,805
by 3  ________
by 5  ________
by 7  ________
by 8  ________
by 9  ________
4.         504
by 2  ________
by 5  ________
by 8  ________
by 9  ________
by 10  ________
5.         801
by 2  ________
by 3  ________
by 4  ________
by 7  ________
by 10  ________
6.         280
by 4  ________
by 6  ________
by 8  ________
by 11  ________
by 12  ________

Classify each number as prime or composite.
7.         82
Prime
Composite
8.         5
Prime
Composite
9.         6
Prime
Composite
10.         58
Prime
Composite
11.         11
Prime
Composite
12.         8
Prime
Composite
13.         36
Prime
Composite
14.         19
Prime
Composite

Use the clue to fill in the missing digit.
15.   The number 14 is divisible by 2.
16.   The number 45 is divisible by 7.
17.   The number 316 is divisible by 9.
18.   The number 45 is divisible by 5.
19.   The number 3 is divisible by 3.
20.   The number 374 is divisible by 6.
21.   The number 300 is divisible by 8.
22.   The number 168 is divisible by 4.

 

Key #2
aKey #2
Complete.
23.   Circle all of the numbers that are multiples of 5.
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3566730273
24.   Circle all of the numbers that are multiples of 3.
4044161121
93882760233

List 3 multiples of each number.
25.  
5





26.  
18





27.  
74





28.  
87





29.  
59





30.  
61






Fill in the missing multiple.
31.  
30, ______, 60, 75, 90
32.  
126, 144, 162, 180, ______
33.  
60, 72, 84, ______, 108
34.  
48, 64, 80, ______, 112
35.  
24, 28, 32, ______, 40
36.  
56, 70, 84, ______, 112

List all of the factors of each number.
37.   48

38.   17

39.   42

40.   96

41.   45

42.   90

43.   93

44.   21

45.   61

46.   76

47.   39

48.   95


 

Key #2
aKey #2
Find the prime factorization of each number.
49.   12

50.   20

51.   32

52.   89

53.   44

54.   79

55.   16

56.   92

57.   41

58.   82

59.   43

60.   50


Find the greatest common factor of each set of numbers.
61.   64 and 32

62.   9 and 33

63.   10, 92, and 4

64.   65 and 5

65.   83 and 29

66.   12, 68, and 40

67.   99 and 22

68.   74 and 31

69.   80 and 95


Find the least common multiple.
70.   5 and 14

71.   7 and 19

72.   2, 6, and 9

73.   3, 6, and 11

74.   4, 6, and 14

75.   2, 10, and 14

76.   3 and 9

77.   10 and 12

78.   11 and 15


Complete.
79.   Identify two numbers whose GCF is 10 and whose LCM is 300. Describe how you found the number.

80.   There are two commutative laws in introductory math: the commutative law of addition and the commutative law of multiplication. What do these two laws have in common? Hint: Write down the equations for the commutative laws of addition and multiplication.


 


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