Prime Factorisation of 729
To find the prime factorisation of 729, we need to break it down into its prime factors, which are numbers that can only be divided by 1 and themselves.

Step 1: Find the Divisible Prime Number
- We start by finding the smallest prime number that can divide 729, which is 3.
- 729 ÷ 3 = 243

Step 2: Continue to Divide by Prime Numbers
- Now we need to continue dividing the result, 243, by prime numbers until we reach 1.
- 243 ÷ 3 = 81
- 81 ÷ 3 = 27
- 27 ÷ 3 = 9
- 9 ÷ 3 = 3
- 3 ÷ 3 = 1

Step 3: Write the Prime Factors
- The prime factors of 729 are all the prime numbers we used in the division: 3 x 3 x 3 x 3 x 3 = 3^6 = 729
Therefore, the prime factorisation of 729 is 3^6. This means that 729 can be expressed as the product of 3 raised to the power of 6.