1. greatest prime number between 1 and 10

Solution:

Number	Factors	Prime or Composite?
1	1	neither Prime nor Composite
2	1,2	Prime
3	1,3	Prime
4	1,2,4	Composite
5	1,5	Prime
6	1,2,3,6	Composite
7	1,7	Prime
8	1,2,4,8	Composite
9	1,3,9	Composite
10	1,2,5,10	Composite

Prime numbers : between 1 and 10
2, 3, 5, 7

There are 4 prime numbers between 1 and 10

Maximum is 7

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2. greatest prime number between 1 and 20

Solution:

Number	Factors	Prime or Composite?
1	1	neither Prime nor Composite
2	1,2	Prime
3	1,3	Prime
4	1,2,4	Composite
5	1,5	Prime
6	1,2,3,6	Composite
7	1,7	Prime
8	1,2,4,8	Composite
9	1,3,9	Composite
10	1,2,5,10	Composite
11	1,11	Prime
12	1,2,3,4,6,12	Composite
13	1,13	Prime
14	1,2,7,14	Composite
15	1,3,5,15	Composite
16	1,2,4,8,16	Composite
17	1,17	Prime
18	1,2,3,6,9,18	Composite
19	1,19	Prime
20	1,2,4,5,10,20	Composite

Prime numbers : between 1 and 20
2, 3, 5, 7, 11, 13, 17, 19

There are 8 prime numbers between 1 and 20

Maximum is 19

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3. greatest prime number between 1 and 50

Solution:

Number	Factors	Prime or Composite?
1	1	neither Prime nor Composite
2	1,2	Prime
3	1,3	Prime
4	1,2,4	Composite
5	1,5	Prime
6	1,2,3,6	Composite
7	1,7	Prime
8	1,2,4,8	Composite
9	1,3,9	Composite
10	1,2,5,10	Composite
11	1,11	Prime
12	1,2,3,4,6,12	Composite
13	1,13	Prime
14	1,2,7,14	Composite
15	1,3,5,15	Composite
16	1,2,4,8,16	Composite
17	1,17	Prime
18	1,2,3,6,9,18	Composite
19	1,19	Prime
20	1,2,4,5,10,20	Composite
21	1,3,7,21	Composite
22	1,2,11,22	Composite
23	1,23	Prime
24	1,2,3,4,6,8,12,24	Composite
25	1,5,25	Composite
26	1,2,13,26	Composite
27	1,3,9,27	Composite
28	1,2,4,7,14,28	Composite
29	1,29	Prime
30	1,2,3,5,6,10,15,30	Composite
31	1,31	Prime
32	1,2,4,8,16,32	Composite
33	1,3,11,33	Composite
34	1,2,17,34	Composite
35	1,5,7,35	Composite
36	1,2,3,4,6,9,12,18,36	Composite
37	1,37	Prime
38	1,2,19,38	Composite
39	1,3,13,39	Composite
40	1,2,4,5,8,10,20,40	Composite
41	1,41	Prime
42	1,2,3,6,7,14,21,42	Composite
43	1,43	Prime
44	1,2,4,11,22,44	Composite
45	1,3,5,9,15,45	Composite
46	1,2,23,46	Composite
47	1,47	Prime
48	1,2,3,4,6,8,12,16,24,48	Composite
49	1,7,49	Composite
50	1,2,5,10,25,50	Composite

Prime numbers : between 1 and 50
2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47

There are 15 prime numbers between 1 and 50

Maximum is 47

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4. greatest prime number between 1 and 100

Solution:
Prime numbers : between 1 and 100
2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97

There are 25 prime numbers between 1 and 100

Maximum is 97

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5. least prime number between 50 and 60

Solution:

Number	Factors	Prime or Composite?
50	1,2,5,10,25,50	Composite
51	1,3,17,51	Composite
52	1,2,4,13,26,52	Composite
53	1,53	Prime
54	1,2,3,6,9,18,27,54	Composite
55	1,5,11,55	Composite
56	1,2,4,7,8,14,28,56	Composite
57	1,3,19,57	Composite
58	1,2,29,58	Composite
59	1,59	Prime
60	1,2,3,4,5,6,10,12,15,20,30,60	Composite

Prime numbers : between 50 and 60
53, 59

There are 2 prime numbers between 50 and 60

Minimum is 53

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6. least prime number between 100 and 110

Solution:
Prime numbers : between 100 and 110
101, 103, 107, 109

There are 4 prime numbers between 100 and 110

Minimum is 101

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