31
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Using the definition that proper factors do not include 1 and the number itself, prime numbers do not have proper factors.
1:
2:
3:
4: 2
5:
6: 2, 3
7:
8: 2, 4
9: 3
10: 2, 5
11:
12: 2, 3, 4, 6
13:
14: 2, 7
15: 3, 5
16: 2, 4, 8
17:
18: 2, 3, 6, 9
19:
20: 2, 4, 5, 10
21: 3, 7
22: 2, 11
23:
24: 2, 3, 4, 6, 8, 12
25: 5
26: 2, 13
27: 3, 9
28: 2, 4, 7, 14
29:
30: 2, 3, 5, 6, 10, 15
31:
32: 2, 4, 8, 16
33: 3, 11
34: 2, 17
35: 5, 7
36: 2, 3, 4, 6, 9, 12, 18
37:
38: 2, 19
39: 3, 13
40: 2, 4, 5, 8, 10, 20
41:
42: 2, 3, 6, 7, 14, 21
43:
44: 2, 4, 11, 22
45: 3, 5, 9, 15
46: 2, 23
47:
48: 2, 3, 4, 6, 8, 12, 16, 24
49: 7
50: 2, 5, 10, 25
The proper factors of 30 are: 1 ,2, 5, 10 and 15. Proper factors are all the numbers that equally go into a number except the number itself! :)
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Why are 3 and 6 excluded?
Out of that list, the only number that has proper factors is 4. The proper factor of 4 is 2.
Of the numbers from 1 to 30, only 30 has all three of those numbers as factors.
Prime numbers don't have proper factors.
There are not common factors of 30 because there cannot be common factors without two or more numbers to compare. Common factors are factors that the numbers being compared have in common. The factors of 30 are 1, 2, 3, 5, 6, 10, 15, and 30. The prime factors of 30 are 2, 3, and 5.
The common factors of 30 and 300 are the numbers that can divide both 30 and 300 without leaving a remainder. The factors of 30 are 1, 2, 3, 5, 6, 10, 15, and 30. The factors of 300 are 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 25, 30, 50, 60, 75, 100, 150, and 300. Therefore, the common factors of 30 and 300 are 1, 2, 3, 5, 6, 10, 15, and 30.
23 is prime. Prime numbers don't have proper factors.