Find the prime factorization of 63
Understand the Problem
The question is asking for the prime factorization of the number 63, which involves breaking the number down into its prime number factors.
Answer
The prime factorization of 63 is $3^2 \times 7$.
Answer for screen readers
The prime factorization of 63 is $3^2 \times 7$.
Steps to Solve
- Divide by the smallest prime number
Start with the smallest prime number, which is 2. Since 63 is odd, it cannot be divided by 2. Next, try dividing by the next smallest prime number, which is 3.
$$ 63 \div 3 = 21 $$
Since 3 is a prime factor, we will keep this in our factorization.
- Continue factorization with the result
Now take the quotient, 21, and divide it by the smallest prime number again. Since 21 is also odd, check with 3.
$$ 21 \div 3 = 7 $$
So, we have another 3 as a prime factor.
- Factor the last result
Now we have 7, which is also a prime number. So, we write down our prime factors.
Adding everything up, we can express 63 as a product of its prime factors:
$$ 63 = 3 \times 3 \times 7 $$
This can also be written using exponents:
$$ 63 = 3^2 \times 7 $$
The prime factorization of 63 is $3^2 \times 7$.
More Information
Prime factorization is useful in many areas of mathematics, including simplifying fractions and finding the least common multiple (LCM) and greatest common divisor (GCD).
Tips
- Forgetting to check for all prime factors: Make sure to check all primes in order, as there could be more than one factor.
- Not recognizing that 7 is a prime number: It’s important to know what qualifies as a prime to avoid skipping valid factors.
