What is the prime factorization of 138?
Understand the Problem
The question is asking for the prime factorization of the number 138, which means we need to express 138 as the product of its prime factors.
Answer
The prime factorization of 138 is $2 \times 3 \times 23$.
Answer for screen readers
The prime factorization of 138 is $2 \times 3 \times 23$.
Steps to Solve
- Divide by the smallest prime number
Start by dividing 138 by the smallest prime number, which is 2.
$$ 138 \div 2 = 69 $$
- Continue with the next prime number
Now, take the quotient 69 and try to divide it by the next smallest prime number, which is 3.
$$ 69 \div 3 = 23 $$
- Check if the last quotient is prime
Now consider the result, which is 23.
Check if 23 is a prime number. Since it has no divisors other than 1 and itself, it is indeed prime.
- Write the prime factorization
Now we can combine all the factors together. The prime factorization of 138 is:
$$ 138 = 2 \times 3 \times 23 $$
The prime factorization of 138 is $2 \times 3 \times 23$.
More Information
138 is an even number, and its prime factorization reveals the basic building blocks of this number. Understanding how to break down numbers into their prime factors helps in various areas of mathematics, such as simplifying fractions and finding least common multiples.
Tips
- Mistaking composite numbers for primes: Ensure all factors are prime; for example, do not include 69 in the final list as it is not prime.
- Overlooking prime numbers: Always remember to check if the final quotient is prime.
