Final answer:
The HCF of 90, 135, and 270 is found by listing their prime factors and identifying the common ones, which are 3 squared and 5, and multiplying them to get 45. Correct option is c) 45.
Step-by-step explanation:
The student is asking what the Highest Common Factor (HCF) of 90, 135, and 270 is. To find the HCF of these numbers, we list out the prime factors:
- 90: 2 × 32 × 5
- 135: 33 × 5
- 270: 2 × 33 × 5
The common prime factors for all three numbers are 32 (which is 9) and 5. Multiplying these together gives us 9 × 5 = 45. Therefore, the HCF of 90, 135, and 270 is 45.