Prime Factorisation of 54: Step-by-Step

Prime factorisation means expressing a number as a product of its prime factors. Prime numbers are numbers greater than 1 that have only two divisors: 1 and themselves.

Calculating Prime Factors for 54

We find the prime factors of 54 by dividing by the smallest prime numbers possible:

• Divide 54 by the smallest prime number, 2: $54 \div 2 = 27$
• Now, factor 27. It is not divisible by 2. The next prime is 3: $27 \div 3 = 9$
• Factor 9. It is divisible by 3: $9 \div 3 = 3$
• The last factor, 3, is a prime number.

So, the prime factorisation of 54 is $2 \times 3 \times 3 \times 3$. The order might differ, but the factors remain the same.

Evaluating Number Factorisation Options

We check each provided option to see which one represents the prime factorisation of 54:

• Option 1: $5.4 \times 10 = 54$. This is not a prime factorisation because 10 is not a prime number and 5.4 is not an integer prime factor.
• Option 2: $3 \times 3 \times 6 = 54$. This is incorrect because 6 is not a prime number.
• Option 3: $9 \times 6 = 54$. This is incorrect because neither 9 nor 6 are prime numbers.
• Option 4: $3 \times 3 \times 3 \times 2 = 54$. All the factors (3 and 2) are prime numbers. This correctly represents the prime factorisation of 54.

The expression $3 \times 3 \times 3 \times 2$ accurately shows the prime factors of 54.