To find the H.C.F. (Highest Common Factor) of 120, 144, and 216, we can use the method of prime factorization.

**Prime Factorization of the given numbers:**

1. 120:
- Start by dividing the number by the smallest prime number, which is 2.
- 120 ÷ 2 = 60
- Now, divide the quotient (60) by 2 again.
- 60 ÷ 2 = 30
- Continue dividing by 2 until the quotient is an odd number.
- 30 ÷ 2 = 15
- 15 is an odd number, so we move to the next prime number, 3.
- Divide 15 by 3.
- 15 ÷ 3 = 5
- 5 is a prime number, so we stop.
- The prime factorization of 120 is 2 × 2 × 2 × 3 × 5 = 2³ × 3 × 5.

2. 144:
- Divide the number by 2 until the quotient is an odd number.
- 144 ÷ 2 = 72
- 72 ÷ 2 = 36
- 36 ÷ 2 = 18
- 18 ÷ 2 = 9
- 9 is an odd number, so we move to the next prime number, 3.
- Divide 9 by 3.
- 9 ÷ 3 = 3
- 3 is a prime number, so we stop.
- The prime factorization of 144 is 2⁴ × 3² = 2 × 2 × 2 × 2 × 3 × 3 = 2⁴ × 3².

3. 216:
- Divide the number by 2 until the quotient is an odd number.
- 216 ÷ 2 = 108
- 108 ÷ 2 = 54
- 54 ÷ 2 = 27
- 27 is an odd number, so we move to the next prime number, 3.
- Divide 27 by 3.
- 27 ÷ 3 = 9
- 9 is an odd number, so we move to the next prime number, 3.
- Divide 9 by 3 again.
- 9 ÷ 3 = 3
- 3 is a prime number, so we stop.
- The prime factorization of 216 is 2³ × 3³ = 2 × 2 × 2 × 3 × 3 × 3 = 2³ × 3³.

**Finding the H.C.F:**

To find the H.C.F., we need to find the highest power of each common prime factor in the given numbers.

The common prime factors in the prime factorizations are 2 and 3.

The highest power of 2 is 2³ = 8.

The highest power of 3 is 3¹ = 3.

Therefore, the H.C.F. of 120, 144, and 216 is 2³ × 3¹ = 8 × 3 =