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.
Similar Questions
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Important Questions from Multiples and Factors
Express 486 as a product of powers of prime factors.
Let p, q, r and s be positive natural numbers having three exact factors including 1 and the number itself. If q > p and both are two-digit numbers, and r > s and both are one-digit numbers, then the value of the expression \(\frac{p-q-1}{r-s}\) is:
Find the greatest three-digit number which is a multiple of 8.
The smallest prime number is:
The sum of three consecutive multiples of 7 is 840. The smallest of these multiples is:
