What are the prime factors of 138?
Understand the Problem
The question is asking for the prime factors of the number 138, which means we need to determine the set of prime numbers that multiply together to give the original number.
Answer
The prime factors of 138 are $2$, $3$, and $23$.
Answer for screen readers
The prime factors of 138 are $2$, $3$, and $23$.
Steps to Solve
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Identify the first prime number Start with the smallest prime number, which is 2. Check if 138 is divisible by 2.
Since 138 is even, it is divisible by 2. We can divide it:
$$ 138 \div 2 = 69 $$
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Check the next prime number Now, we need to factor 69. The next prime number is 3. Check if 69 is divisible by 3.
The sum of the digits of 69 is $6 + 9 = 15$, which is divisible by 3. So, we divide:
$$ 69 \div 3 = 23 $$
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Check for further factors Now we have 23. Check if 23 is a prime number. It is not divisible by 2, 3, or 5, and since it's less than 24, it is a prime number.
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List the prime factors The prime factorization of 138 can now be written as:
$$ 138 = 2 \times 3 \times 23 $$
The prime factors of 138 are $2$, $3$, and $23$.
More Information
The process of finding prime factors involves dividing the original number by the smallest prime numbers until all resulting factors are prime. This process is fundamental in number theory. The number 138 is a composite number, which means it can be expressed as a product of prime factors.
Tips
- A common mistake is to think the number is prime without checking all smaller primes. Always check divisibility against smaller primes first.
- Another mistake is not performing the division correctly, leading to incorrect factors. It helps to double-check the arithmetic.
