What are the prime factors of 378?
Understand the Problem
The question is asking for the prime factors of the number 378. To solve this, we will identify the prime numbers that multiply together to give 378.
Answer
The prime factorization of 378 is $2 \times 3^3 \times 7$.
Answer for screen readers
The prime factors of 378 are $2$, $3$, and $7$, and the complete prime factorization is $378 = 2 \times 3^3 \times 7$.
Steps to Solve
- Start with the number 378
We will begin the prime factorization by dividing 378 by the smallest prime number, which is 2.
- Divide by 2
Since 378 is an even number, we can divide it by 2:
$$ 378 \div 2 = 189 $$
Now we have 189.
- Next prime number, check divisibility by 3
Now we will check the next smallest prime number, which is 3. Adding the digits of 189 gives us $1 + 8 + 9 = 18$, which is divisible by 3. Therefore, we can divide:
$$ 189 \div 3 = 63 $$
- Continue dividing by 3
We will continue to divide by 3 since 63 is also divisible by 3:
$$ 63 \div 3 = 21 $$
- Divide once more by 3
Again, 21 is divisible by 3:
$$ 21 \div 3 = 7 $$
- Identify the last factor
Now we are left with the number 7, which is a prime number itself.
- Compile the prime factors
The prime factorization of 378 can now be written as:
$$ 378 = 2 \times 3^3 \times 7 $$
The prime factors of 378 are $2$, $3$, and $7$, and the complete prime factorization is $378 = 2 \times 3^3 \times 7$.
More Information
The prime factorization of numbers helps in various mathematical applications, including simplifying fractions and finding least common multiples. Prime numbers are numbers greater than 1 that have no divisors other than 1 and themselves.
Tips
- Not checking for the smallest prime number first or jumping to larger primes.
- Forgetting to check if the results of divisions are prime.
