1. **State the problem:** Find the prime factorisation of 44. 2. **Start with the smallest prime number:** 2. Check if 44 is divisible by 2. 3. Since 44 is even, divide by 2: $$44 \div 2 = 22$$. 4. Check if 22 is divisible by 2 again: $$22 \div 2 = 11$$. 5. Now, 11 is a prime number and cannot be divided further by any prime other than itself. 6. **Write the prime factorisation:** The prime factors of 44 are 2, 2, and 11. 7. Using index notation, this is written as $$2^2 \times 11$$. **Final answer:** $$44 = 2^2 \times 11$$