Find the highest common factor of 405 , 783, 513

Solution:
1. Factorize 405:
- 405 = 3 × 135
- 135 = 3 × 45
- 45 = 3 × 15
- 15 = 3 × 5
- Therefore, 405 = 3^4 × 5

2. Factorize 783:
- 783 = 3 × 261
- 261 = 3 × 87
- 87 = 3 × 29
- 29 is prime.
- Therefore, 783 = 3^3 × 29

3. Factorize 513:
- 513 = 3 × 171
- 171 = 3 × 57
- 57 = 3 × 19
- 19 is prime.
- Therefore, 513 = 3^3 × 19

4. Find the common prime factors:
- The common prime factor among 405, 783, and 513 is 3.

5. Identify the lowest power of the common factor:
- The lowest power of 3 common to all factorizations is 3^3.

6. The highest common factor (HCF) is therefore:
3^3 = 27