Write the prime factorization of 54
Understand the Problem
The question is asking for the prime factorization of the number 54, which involves breaking down the number into its prime factors.
Answer
The prime factorization of 54 is \( 2 \times 3^3 \).
Answer for screen readers
The prime factorization of 54 is ( 2 \times 3^3 ).
Steps to Solve
- Start with the number 54
We need to find the prime factors of 54. First, we check for the smallest prime number, which is 2.
- Divide by the smallest prime (if applicable)
Since 54 is even, we can divide it by 2:
$$ 54 \div 2 = 27 $$
So, we have one prime factor: 2.
- Continue with the resulting number (27)
Now we need to factor 27. The next smallest prime number is 3. We check if 3 divides 27:
$$ 27 \div 3 = 9 $$
Thus, we have another prime factor: 3.
- Factor further (9)
Next, we factor 9 (which we got from our previous result) by dividing it again by 3:
$$ 9 \div 3 = 3 $$
This gives us another prime factor: 3.
- Final factorization step (3)
Now, we have 3 left, which is a prime number. So, we stop here.
- Combine the prime factors
Putting it all together, the prime factorization of 54 is:
$$ 54 = 2 \times 3 \times 3 \times 3 $$
This can also be expressed as:
$$ 54 = 2 \times 3^3 $$
The prime factorization of 54 is ( 2 \times 3^3 ).
More Information
The prime factorization shows us how to express a number as the product of its smallest prime factors. Prime factorization is useful in various areas of mathematics, including simplifying fractions, finding least common multiples, and solving problems related to divisibility.
Tips
- Forgetting to check if a number is divisible by smaller prime numbers before moving on to larger ones. It's essential to start from the smallest prime, 2, and work upwards.
- Miscounting the occurrences of a prime factor, especially when the same prime factor appears more than once.
