Working.

To calculate the sum of prime factors between 10 and 30, we first need to find the prime factors of each number between 10 and 30.

Prime factors of numbers between 10 and 30:
- 10: 2, 5
- 11: 11
- 12: 2, 3
- 13: 13
- 14: 2, 7
- 15: 3, 5
- 16: 2
- 17: 17
- 18: 2, 3
- 19: 19
- 20: 2, 5
- 21: 3, 7
- 22: 2, 11
- 23: 23
- 24: 2, 3
- 25: 5
- 26: 2, 13
- 27: 3
- 28: 2, 7
- 29: 29
- 30: 2, 3, 5

Now, we sum up all the unique prime factors:
2 + 3 + 5 + 7 + 11 + 13 + 17 + 19 + 23 + 29 = 109

Therefore, the sum of prime factors between 10 and 30 is 109.

1. 10 = 2 - 5
2. 11 = 11
3. 12 = 2 - 2 - 3
4. 13 = 13
5. 14 = 2 - 7
6. 15 = 3 - 5
7. 16 = 2 - 2 - 2 - 2
8. 17 = 17
9. 18 = 2 - 3 - 3
10. 19 = 19
11. 20 = 2 - 2 - 5
12. 21 = 3 - 7
13. 22 = 2 - 11
14. 23 = 23
15. 24 = 2 - 2 - 2 - 3
16. 25 = 5 - 5
17. 26 = 2 - 13
18. 27 = 3 - 3 - 3
19. 28 = 2 - 2 - 7
20. 29 = 29

Prime factors between 10 and 30 are:

2, 3, 5, 7, 11, 13, 17, 19, 23, 29

Sum of prime factors between 10 and 30 =

2 + 3 + 5 + 7 + 11 + 13 + 17 + 19 + 23 + 29 =-- 131