What are the prime factors of 180?
Understand the Problem
The question is asking for the prime factors of the number 180. This requires breaking down the number 180 into its prime components, which are the prime numbers that can be multiplied together to result in 180.
Answer
The prime factors of 180 are $2^2 \times 3^2 \times 5$.
Answer for screen readers
The prime factors of 180 are $2^2 \times 3^2 \times 5$.
Steps to Solve
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Start with the number 180
To find the prime factors of 180, we begin by dividing it by the smallest prime number, which is 2. -
Divide by 2
Since 180 is even, we can divide it by 2:
$$ 180 \div 2 = 90 $$ -
Continue dividing by 2
Now, we take the result (90) and divide it by 2 again:
$$ 90 \div 2 = 45 $$ -
Switch to the next prime number
Since 45 is not even, we cannot divide by 2 anymore. We move to the next prime number, which is 3:
$$ 45 \div 3 = 15 $$ -
Continue with 3
Next, we divide 15 by 3:
$$ 15 \div 3 = 5 $$ -
Identify the last prime number
Now we have reached 5, which is already a prime number. So we stop here. -
Collecting all prime factors
The prime factors of 180 are the prime numbers we used in our division:
So, the complete prime factorization of 180 is:
$$ 2^2 \times 3^2 \times 5 $$
The prime factors of 180 are $2^2 \times 3^2 \times 5$.
More Information
The number 180 can be expressed in different ways using its prime factors. Understanding prime factorization is essential in mathematics, particularly in number theory, and helps in simplifying fractions and finding least common multiples and greatest common divisors.
Tips
- Forgetting to check for divisibility by prime numbers in order, which can lead to missed factors.
- Not recognizing that once you reach a prime number you can stop dividing.
