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Page 1 of 4
Date ___________________
Name _____________________________
(Answer ID # 0424844)
Number Theory
Classify each number as prime or composite.
1.
2.
90
14
Prime
Prime
Composite
Composite
5.
42
Prime
Composite
6.
34
Prime
Composite
3.
23
4.
Prime
Composite
7.
92
Prime
Composite
41
Prime
Composite
8.
5
Prime
Composite
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.
9.
10.
11.
12.
171
84
2,584
2,617
by 3 ________
by 2 ________
by 4 ________
by 3 ________
by 5 ________
by 4 ________
by 7 ________
by 5 ________
by 6 ________
by 5 ________
by 8 ________
by 6 ________
by 8 ________
by 6 ________
by 11 ________
by 9 ________
by 9 ________
by 10 ________
by 12 ________
by 13 ________
Use the clue to fill in the missing digit.
13. The number 117
is divisible by 13.
15. The number 47
17. The number 1
19. The number 121
14. The number
66 is divisible by 7.
is divisible by 17.
16. The number 89
6 is divisible by 11.
64 is divisible by 8.
18. The number 57
7 is divisible by 19.
is divisible by 9.
List all of the factors of each number.
21. 34
22. 22
20. The number
64 is divisible by 6.
23. 33
24. 97
25. 45
26. 15
27. 26
28. 72
29. 31
30. 49
31. 79
32. 63
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Find the prime factorization of each number.
33. 16
34. 32
35. 37
36. 66
37. 21
38. 59
39. 68
40. 51
41. 12
42. 15
43. 45
44. 74
Find the greatest common factor of each set of numbers.
45. 50 and 30
46. 90 and 40
47. 94 and 84
48. 43 and 41
49. 21 and 51
50. 40, 72, and 96
51. 36, 90, and 27
52. 22 and 55
53. 95 and 85
Find the least common multiple.
54. 6 and 14
55. 8 and 15
56. 6 and 22
57. 2, 8, and 14
58. 6, 8, and 10
59. 6 and 10
60. 5 and 17
61. 9 and 15
62. 8 and 18
Complete.
63. Use the digits 8, 4, 6, and 0 to create a 4-digit 64. If the sum of the digits of a number is
number that is divisible by 2, 3, 4, 5, 6, 8, and
divisible by three, then the number itself is
9. Describe how you found the number.
divisible by three. If the sum of the digits of a
number is divisible by nine, then the number
itself is divisible by nine. For example 36 is
divisible by both 9 and 3 because 6 + 3 = 9,
and 9 is divisible by both 3 and 9. Are all
numbers that are divisible by 3 also divisible
by 9? Why or why not?
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Answer Key 0424844
Classify each number as prime or composite.
1.
90
2.
Prime
Composite
5.
42
Prime
Composite
3.
14
Prime
Composite
6.
23
4.
Prime
Composite
7.
34
Prime
Composite
92
Prime
Composite
41
Prime
Composite
8.
5
Prime
Composite
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.
9.
10.
11.
12.
171
84
2,584
2,617
by 3
yes
by 2
yes
by 4 yes
by 3
no
by 5
no
by 4
yes
by 7 no
by 5
no
by 6
no
by 5
no
by 8 yes
by 6
no
by 8
no
by 6
yes
by 11 no
by 9
no
by 9
yes
by 10
no
by 12 no
by 13
no
Use the clue to fill in the missing digit.
13. The number 117
is divisible by 13.
15. The number 47
1170 14. The number
or: 966
66 is divisible by 7.
266
is divisible by 17.
476 16. The number 89
6 is divisible by 11.
8976
17. The number 1 64 is divisible by 8.
or: 1264, 1464, 1664, 1864
1064 18. The number 57
7 is divisible by 19.
5757
19. The number 121
1215 20. The number
or: 264, 864
is divisible by 9.
List all of the factors of each number.
21. 34
22. 22
1, 2, 17, 34
1, 2, 11, 22
64 is divisible by 6.
23. 33
1, 3, 11, 33
24. 97
1, 97
564
25. 45
1, 3, 5, 9, 15, 45
26. 15
1, 3, 5, 15
27. 26
1, 2, 13, 26
28. 72
1, 2, 3, 4, 6, 8, 9,
12, 18, 24, 36, 72
29. 31
1, 31
30. 49
1, 7, 49
31. 79
1, 79
32. 63
1, 3, 7, 9, 21, 63
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Answer Key 0424844
Find the prime factorization of each number.
33. 16
2x2x2x2
34. 32
2x2x2x2x2
35. 37
1 x 37
36. 66
2 x 3 x 11
37. 21
3x7
38. 59
1 x 59
39. 68
2 x 2 x 17
40. 51
3 x 17
41. 12
2x2x3
42. 15
3x5
43. 45
3x3x5
44. 74
2 x 37
Find the greatest common factor of each set of numbers.
45. 50 and 30
46. 90 and 40
10
10
47. 94 and 84
2
48. 43 and 41
1
49. 21 and 51
3
50. 40, 72, and 96
8
51. 36, 90, and 27
9
52. 22 and 55
11
53. 95 and 85
5
Find the least common multiple.
54. 6 and 14
55. 8 and 15
42
120
56. 6 and 22
66
57. 2, 8, and 14
56
58. 6, 8, and 10
120
59. 6 and 10
30
60. 5 and 17
85
61. 9 and 15
45
62. 8 and 18
72
Complete.
63. Use the digits 8, 4, 6, and 0 to create a 4-digit 64. If the sum of the digits of a number is
number that is divisible by 2, 3, 4, 5, 6, 8, and
divisible by three, then the number itself is
9. Describe how you found the number.
divisible by three. If the sum of the digits of a
number is divisible by nine, then the number
itself is divisible by nine. For example 36 is
divisible by both 9 and 3 because 6 + 3 = 9,
4,680
and 9 is divisible by both 3 and 9. Are all
numbers that are divisible by 3 also divisible
by 9? Why or why not?
No. The easiest way to show this is by
considering the number 6. Six is clearly
divisible by 3 but not by 9. There are many
other examples. Thirty-three is divisible by
3 because 3 + 3 = 6, which is divisible by 3.
But 33 is not divisible by 9.
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