What is the prime factorisation of 144?
Understand the Problem
The question is asking for the prime factorization of the number 144, which means we need to determine the prime numbers that multiply together to give 144.
Answer
The prime factorization of 144 is $2^4 \times 3^2$.
Answer for screen readers
The prime factorization of 144 is $2^4 \times 3^2$.
Steps to Solve
- Start with the number 144
We begin by dividing 144 by the smallest prime number, which is 2.
$$ 144 \div 2 = 72 $$
- Continue factoring using prime numbers
Next, we continue factoring 72 by dividing it again by 2.
$$ 72 \div 2 = 36 $$
- Repeat the process with 36
We can divide 36 by 2 one more time.
$$ 36 \div 2 = 18 $$
- Keep factoring with 18
Continue factoring 18 by dividing by 2.
$$ 18 \div 2 = 9 $$
- Switch to the next prime number
Now, since 9 is not divisible by 2, we switch to the next prime number, which is 3.
$$ 9 \div 3 = 3 $$
- Finish with the last prime factor
We divide the last 3 by itself.
$$ 3 \div 3 = 1 $$
- Combine the factors
Now we can express the prime factorization of 144 as:
$$ 144 = 2^4 \times 3^2 $$
The prime factorization of 144 is $2^4 \times 3^2$.
More Information
The prime factorization helps us understand the basic building blocks of a number. In the case of 144, it shows that it can be constructed using the prime numbers 2 and 3. This factorization is also useful in simplifying fractions and solving equations.
Tips
- Forgetting to check if the resulting quotient can be further factored down into prime numbers.
- Stopping the factorization too early; always ensure you've reached 1 after continuous division by prime numbers.