Find the Highest Common Factor (H.C.F) of 108, 288 and 360.

108, 288 and 360.

Prime Factorization;

108 = 2 × 2 × 3 × 3 × 3 = $$2^2 \times 3^3$$​​
288 = 2 × 2 × 2 × 2 × 2 × 3 × 3 = $$2^5 \times 3^2$$​​
360 = 2 × 2 × 2 × 3 × 3 × 5 = $$2^3 \times 3^2 \times 5$$

The common prime factors of 108, 288, and 360 are 2 and 3.

For 2, the smallest power is $$2^2$$​.
For 3, the smallest power is $$3^2$$​.
​$$H.C.F. = 2^2 \times 3^2 = 4 \times 9 = 36$$

Thus, the correct answer is (b).